That's not really the case in all of the Ars canon, your saga may vary, but magi, before the Order, were often distrustful towards other magi. It's a big part of the story of why it took so long for Trianomae to gather magi together and join Bonisagus. Parma blocking the effects of another's Gift is also a reason why the magi of the Order form covenants and come together, while hedge mages don't work together very often. The Order of Suleiman might be the exception, but I will be honest that I haven't digested all of The Crescent and the Cradle. In short, you blow away a lot of history of how and why the Order was founded. It wasn't just a unified Magic Theory, it was also the Parma Magica.
Covenfolk can become used to the Gift over time. Covenants suggests 15 years for normal, and 30+ for Blatant. I think there can be modifiers to that, too.
Over time people can become accustomed to the gift of particular magi,they don't stop feeling it but they tend to ignore it. There are rules for abstractly calculating covenfolk loyalty in covenants, I'm not certain that they make for good stories if used in play (haven't used them) but they make a detailed description of how the line at least thinks about the effects of the gift on organizations.
You think that the setting would be more believable if it were so rather than the way it is presented? I suppose it could be. Obviously if we change the setting to conform to your second point -that gifted folks don't disturb one another- then your first point naturally follows.
Do you have any particular ideas about stories that could be told with your modified setting ?
It is, as Jonathon mentioned, possible for characters to grow accustomed to the gift or "their" magi with enough exposure. It's also hinted at a few places that simply being aware that the dislike is supernatural in origin can be sufficient to mitigate the effects of The Gift to some extent - the grogs still won't like the magus, but at least they'll realize it's not his fault.
As for non-hermetics, of the traditions described in various 5E supplements only 7 actually require The Gift: Hermetic Magi, Vitkir, Amazon Sorceresses, Augustan Wizards, Muspelli, Soqotran Sorcerers, and Storm Wizards. Also, Gifted Sahir are able to use their Storytelling Magical Defense to eliminate the social aspects of The Gift...
The Sihr can't eliminate the initial effects, but they can override the later effects with their abilities, and change the person's mind. Especially if they start forcing positive warping experiences. Sort of like you have a conversation with Hitler and come away realizing he's a really great guy, and you should totally do his dirty work for him free of charge! I believe the Vitkir can also give themselves bonuses to social rolls to override the later effects. The Gifted Learned Magicians I think can grant themselves virtues, like say.. Gentle Gift.
Otherwise wizard's do absolutely suffer effects of the Gift, although arguably with training they can learn to overcome it. I know there have been studies where people respond vastly differently to drugs if they know what they got given.
For me, the gift not disturbing other gifted, is more of a flavour in the saga; rather than telling specific stories about the modified gift; you could make a story with themes of closeness i.e "the world doesn't really accept or understand us" so the Magi are united against the outside world?
It just makes more sense that the magic resistance quality of Parma would be the largest factor in magi meeting & cooperating, like in the founding 12 houses.
I don't know, the "Magical Defenses" box on page 48 seemed pretty clear to me that a sahir receives a bonus equal to the Magnitude of his Storytelling ability on die rolls related to non-magical social interaction. One could, of course, argue that the effect is tainted by The Gift in a sort of terror and awe rather than actual friendship, but the net effect is that Gifted sahir are able to cooperate so long as their leader has a decent Storytelling score.
If a mage extends their Parma to a mundane do they immediately notice the removal of the effect of the Gift? If so, does that mean they can remember the experience after the Parma is withdrawn? It might help convince them (or it might make them more worried when it is withdrawn).
But only when the Gift wasn't making them uncomfortable! Actually, if the maga is a sneaky little bastard she can grab'em before they notice her and get Gifted. She'll get a reputation for stealth glomps, but no Gift related social issues. That said, she'll probably develop a non-Gift bad reputation so it won't really help.
Also note that the Gift doesn't kick in if the magus isn't interacting socially - if they're just standing at the far side of a room, or behind their grog while the grog does the talking for them, then there's no penalty to a Social roll. (ie, because there's no social interaction to penalize). So, technically, a magus could just walk up to someone and extend their parma, in the same way that someone could walk up to a stranger and punch them in the face, without socially interacting with them. However, the body language required to NOT engage someone socially (essentially to treat them like an object) while extending the parma may very well have that -3 penalty in there, anyway. As others have noted, the Gift is tenacious that way.
At the least, the target would wonder what the heck just happened, as the scholar completely ignored them for the beginning of the conversation, muttered a few words in latin under their breath, then suddenly became a lot more personable.
Because I've always been under the impression that the Gift's effect simply requires the individual to be aware of the magus's presence. ie. a Mage walks into a bar, and people who notice him just tend to assume he's somewhat shifty, he just gives off the wrong vibes.
Ars Magica 5, Page 75, third column, fourth paragraph: "If a Gifted maga dresses unostentatiously, keeps to the middle of the group, does not appear to be the leader, and doesn’t talk to anyone, then the group should be able to travel without suffering from people’s reactions to The Gift, as long as the maga behaves herself. The Blatant Gift makes this a lot harder; these precautions reduce people’s reactions to those inspired by the normal Gift."
It's not that the Gift doesn't kick in, but that people don't actually interact with the magus in any meaningful way, so the penalties don't apply. Of course if a magus enters a bar, that by itself is interacting with at least the bartender, since it is his job to be aware of the patrons. But if a large party of non-Gifted grogs accompanies the magus, and he uses the precautions mentioned above, the bartender might not notice enough to act differently toward the grogs.
One thing to remember is that the social effects of The Gift aren't just generic bad vibes and a -3 modifier. The Gift specifically engenders feelings of mistrusts and envy and these produce the mechanical -3 penalty. An effect tailor made to be difficult to overcome by either mundane or magical means. To those that feel it's effects the gifted seem to be perpetually up to something in possession of things you should have.
Even when you counter the mechanical effects with some other bonus the subtext should still be present in the RP. And magical or other temporary effects are likely to have a big rebound when the wear off. Heck even when a gifted character doesn't use magic and does something that naturally engenders good feelings NPC's could just assume it's a trick. It does take 15 years to overcome the penalty.
Now double all those problems and imagine two Gifted characters trying to work together without the consistent use of Parma.