I am trying to think of a modern analogue to the AotH.
You and your sodales have a company headquarters where all your valuable data/commercial info/research materials and confidential work happens, with the HQ being a secured facility.
If you invite a competitor over for a meeting, do you grant them an Access-all-areas pass?
That's not really what it is, because really senstive places within the covenant could be protected in other ways, e.g. a Watching Ward, and visitors could be guarded and explicitly forbidden from straying from their rooms, the council chamber or other common areas. A casting token does not necessarily grant a visitor all the rights of a member of the covenant.
I think only extremely paranoid and anti-social magi would hold that little speech. One of the raisons d'etre of the Order of Hermes is to enable magi to get along, co-operate and meet each other on equal terms, without any fear of being attacked with magic. I believe that is one of the main purposes of the Parma Magica, and I think casting tokens serve that purpose too.
Also, turn the situation around and think about player character magi visiting another covenant for whatever reason. Never mind NPC quaesitores or hoplites. It seriously limits what the players can do if their magus PCs don't have casting tokens.
I very much doubt that. Take a look at TCI p.6 and you will see the angle of the speaker. If that isn't enough, look at p.15 The Siege of Praesis, especially the attempt of Holzner.
In other words, mages. There is a reason players have Companion characters; and that reason is that mages are (by design) extremely bad at social interactions.
Yes, and another reason as well: To protect the magical secrets of members from theft. The Aegis of the Hearth serves both purposes -- it protects everyone inside from hostile supernatural activity. Visitors, with or without casting tokens, benefit from this; and allowing someone to shelter inside the Aegis is a valuable aspect of hospitality. Protecting the magical secrets of mages of the covenant is also important, and giving away a casting token makes the Aegis powerless.
A third reason the Order of Hermes exists is to promote trust among members; allowing mages to form trusted groups that can act together. This grants a group of OoH mages who have developed such trust an advantage of numbers against all rival magic traditions, and is a great source of strength of the Order as a whole. Those trusted groups are called 'covenants'; and a visitor to a covenant can be expected to be trusted less than covenant members -- after all, if they were equally trusted then they would (usually) be members.
Your Saga May Vary, but I think it is entirely reasonable that showing up on the doorstep (or even visiting for a season to copy or study a book) does not involve receiving a casting token.
Exactly this. It is the primary security measure against foreign magic that most Covenants possess. Giving a token to someone therefore seems intrinsically an indication of high trust to me. Or simply a mindset that is not serious at all about security (which, granted, that is not so uncommon an attitude).
Why? Do you give everyone you invite to your home a house key to use while they are there? I am willing to wager the answer is no, right?
The Order is not perfectly stable or peaceful. The fact that it is a largely functioning magical society at all is effectively a miracle in the setting. But that doesn't mean it is an overarchingly high trust society where no one locks their doors (so to speak). In fact we have descriptions of multiple Tribunals that give exactly the opposite impression, where building up a Covenant as a strong institution able to defend itself, including against other Covenants and their competing interests, is an essential part of the survival of any Covenant. That isn't "anti-social" it is simply pragmatic and dealing with the fact that Magi simply do not always get along any more than other type of person does.