It's an established fact in ArM that the Church, a socio-political entity that calls out Crusades against entire demographics, is aware of the Order of Hermes. Since the standard assumes that covenants aren't monasteries in disguise, what excuses should be used for the Church to not declare war against the Order? This is an organization of people with explicit & obvious magic powers that aren't derived from God (Leviticus is relevant here), and in fact have a pagan deity in their own title.
Same reason America doesn't declare war on Russia: THE'VE GOT NUKES! 
On the positive side, the Church is aware of the Order, but not sure of it. Although magi are often a suspicious lot, the magi the Church encounters most often is not (Gently Gifted House Jerbiton). The Order may be a threat, but they aren't actively menacing or directly spiritually corrupting, unlike Saracens and Cathars, and they do not greatly challenge the power structure. Indeed, they might be recruited to support the goals of the Church. In some cases, magi of the Order have supported Church and Crown against heretics, invaders, demon-worshipers, and other mutual threats.
On the negative side, the Order is reported to have vast magic powers, which they seem to have not used much, to blight crops, blast regions, burn cities, and bend minds. God is almighty, and the victory of the Church in a Crusade is inevitable, and the dead and cursed will find favor in His sight, but why pick a fight with an apparently low priority threat?
That said, there are, I am sure, churchmen who push hard for a crusade against the Order, and magi who push hard for war on the Church, but they're a fanatic fringe.
It is a mistake to think the church is the sole cause of the Crusades. In every instance, there are political and economic factors in play, as well as the influence of secular powers. So the answer is that there is no real profit or advantage to be gained by declaring war on the Order.
Also, in the real world there is no such thing as wizards or magic. But in the fictional game world, there is. So it is reasonable to presume that matters would be interpreted differently. No hazard in burning witches at the stake because the cannot shoot back, not in reality. But in fiction they can. Too much risk, nothing to be gained.
You can thank House Flambeau for keeping you all safe 
Which brings up an interesting variation in the near future of AM:
in LOM it is spelled out "It is the opinion of the Order that when someone declares all magi his enemy, he may be taken at his word."
in the real world professional witch hunters would make such proclamations before turning their attentions to defenseless innocents. In the world of AM, if such a witch hunter was near, I would expect they would find their career greatly foreshortened by magi acting upon his threats.
That seems like a bit of a cop-out though. The Church certainly had economic/political factors, but the idea of sorcerers openly practicing magic without consequence in otherwise historically accurate 13th century Europe is a rather large plot hole that deserves more treatment than "they don't feel like it."
I'm talking an entire article dedicated to such historic events as the Paderborn Proclamation, the writings of the Lombard Archives, and the Crusade of Worms. Write up additional Peripheral Code rulings, detail historic Hermetic diplomats, possibly even a now-lost Fenicil ritual.
Our campaign solves this mostly by magi not being... excessively open. The nobility is vaguely aware, the church has some ideas, but it's partly a case of "we can't prove it, and without proof, we could end up causing a schism in the church rather than a crusade."
Crusades work a lot better when there is significant land or wealth to be seized. Magi seldom have much land - and often it's land that's weird/cursed/scary, and a covenant's wealth isn't in silver.
Don't forget, too, that the clergy in Mythic Europe have far bigger fish to fry, like ACTUAL demons and faeries causing all manner of problems. Only when magi are causing problems on the same scale as these will they draw serious attention.
A crusade usually needs to be declared against a specific geographic area, while the Order of Hermes is scattered all over Mythic Europe. A more likely thing would be the Pope ordering the Order condemned as anathema a la the Templars, which would likely be solved by either that pope or his replacement mysteriously changing his mind. (MR 25 is not that hard to overcome.)
Just to add my two cents...
One thing that my students have been learning recently is that the church doesn't automatically call crusades against those who oppose its teachings. What tends to provoke crusades is when the individual or group in question explicitly reject the value of the church as a necessary part of God's plan for salvation and/or, as some have noted, political or economic consequences of this. It is interesting to compare for example, the Franciscans to the Cathari:
The Franciscans came into being as a movement that opposed the wealth of the church and wanted to return to the poverty that they saw as being part of the lifestyle of Jesus and the disciples, but St Francis was careful to place his order under the control of the pope, and it became an accepted part of the established church (some Franciscans did get in trouble later, but that's another story). The Cathari, on the other hand, rejected the established church as being necessary for the salvation of Christians, and when the movement spread, encompassing much of southern France and attracting the patronage of nobles, they became a threat to the church's interests in the region, including its political clout and economic resources. So one could say that it was their rejection of the church, which had real economic and political implications because of how widespread the Cathari were, that led to the crusade rather than their heresy in and of itself. Of course some in the Catholic Church were concerned for the souls of the people of southern France, but that was arguably secondary to the other concerns.
So in other words, covenants are far more likely to be attacked by crusaders if the church wants either their resources or to reduce their influence than if the covenants' members are not good Catholics.
Of course, it's possible the Church might declare a crusade against magi, possibly just the magi of a given area. Fighting that out might be fun, but it's a wrecker for Mythic Europe.
It's also possible that the Church and Order might ally in the face of the Mongols or Moors.
These are considerations for long term stories, and generally magi of a few decades experience, I should think.
The crusade after the assassination of a papal legate was called to subdue the whole country, nobles and towns, not just the Cathars in it. Crusader armies, composed of 40 days volunteers, were not investigators and could not make any distinction.
The Cathars in Northern Italy were no less vocal or entrenched than their Occitanian brothers, but nobody considered calling a similar crusade against cities like Milan, Parma, Verona or the Cathar bishoprics near Lake Garda.
:mrgreen:
Cheers
Additonally, I have assumed that the main activity of most of the Trianomae has been in the area of 'relations with church and crown'. Therefore, there has been quite a lot of doctoring of evidence and people's opinions going on so the Order doesn't get targetted.
One game I have heard about played out a major war between magi and the church, where the corrupt pope & cardinals ended up opening a massive Hellgate underneath the Vatican...that campaign didn't exactly follow mundane history very much!
Don't forget the Jerbitons. Trianomae are more focused on lubing the gears within the Order.
Or a covenant or Tribunal might ally with or even offer tribute to the Mongols. It worked for Alexander Nevsky...
Perhaps. It might just be me, but I tend to see House Jerbiton mostly caring about House Jerbiton, whereas the Trianomae actively work for the 'good' of the whole Order. Therefore, I can see Jerbiton magi having very good relationships with any mundane authorities in their vicinity, but not really caring much if the Church as a whole dislikes what the Order is up to in, say, northern Germany. Trianomae I see as being the other way around - not caring too much about individual magi or covenants, but working to prevent the Church doing anything about the whole Order.
Both would have agents within/near the cardinals, and they'd probably cooperate most of the time.
Anyway, that's my take on it.
To an extent, or at least to the extent that stereotypes about any House are true, I'd be inclined to agree that magi Trianomae are more reliably concerned with working for the good of the Order than Jerbitons (though I disagree that magi Jerbiton care much about their House either; their main interests are individual). However, I very much doubt that Trianomae even agree that the Order should have any consistent contact with mundanes at all; I imagine that there's plenty of magi Trianomae who don't agree that the Order should have any contact with mundanes at all; the Rhine Tribunal is still the heart of House Bonisagus, and about half of the magi there operate on a principle of blasting mundanes into drifting ash whenever they encroach on the Order's interests, so plenty of Trianomae probably see the muggles as generally beneath their notice.
Jerbiton magi are actively involved in mundane affairs by virtue of being Jerbiton, so I imagine that if a Tribunal needs to deal with church and crown, they'll turn the job over to the local Jerbitons. It's an open question whether any individual Trianoma will have this as an interest, even if they're more likely to be equipped for the task than your average Merinita.
With respect to Trianomae, don't forget that there are not a lot of them. Serf's Parma, I'm thinking About the same as Merceris magi.
Yep, very true.
If only just for the fact of Gentle Gift. HoH: Societas (p55) is suggesting that Jerbiton magus are putting a premium on being able to interact with mundanes, thus are willing to compromise with other short-comings (flaws or lower caracteristics) that other House would find crippling and disqualified the gifted kid to become an hermetic magus.
Trianoma magus with gentle gift are probably very rare, so for this reason, Jerbitons are likely the contact point of the mundane world with the Order of Hermes.
Mechanically, the Gift gives a -3 penalty on all social rolls, so technically it can be offset by high skills level, boosted by some specific spells (variant of Aura of Enobled Presence and such). Yet, if we look beyond the mechanical aspect, the Gift leaves a feeling of unease and distrust which cannot be permanently altered by spells or skills. So considering how dire could be consequence of a faux-pas during negotiation with member of the Church, which sane magus would take the risk if they can avoid by asking assistance from a fellow sodales of House Jerbiton
?
No matter how innocuous is a spell, if a group of mundane is convinced that a spell was cast on them during discussion, whatever agreement was reached will be torn to pieces. Who will be willing to listen and believe a magus who is trying to explain that because of the magical energy flowing through his body, people are uncomfortable in his presence, thus he casted a spell just to avoid annoying guests ? That's will sound convoluted and probably hidding some less noble reasons.
HOH:TL, p. 5 - there are ~29. Not a lot of them, but more than twice as many as Magi Merceri.
Per HoH:TL 16, Trianomae favor the Gentle Gift as well, albeit not as strongly as the Jerbitons do (of course, magi Trianomae can have their pick of apprentices, too-but yes, there's not a lot of 'em).
The reason Jerbitons are the contact point of the Order with the mundane world is because they're the societas that's focused on mundane society. They'll have connections with the mundane nobles, clergy and scholars well before the Order actually has need of their services. It's what they do.