Solicits for August say: "Logan leads his own team of classic X-Men into battle!"
So I suspect the X-Men at the Jean Grey school don't seem to have a problem with Wolverine either.
If anything, I think the people the X-Men will have problems with after AvX will likely be members of the Extinction Team, not Wolverine. The issue here really isn't the X-Men have a problem with Logan... it's simply that you do. And the reason for that is simply that they understand the character even if you don't.