People made fun of Ute fans for the PAC12 tattoos, bumper stickers, clothing, etc.
I don't recall too much finger-pointing or laughing at Ute fans cheering for other PAC12 teams.
Any talk about "PAC12 Country" was pretty limited - and tended to piggyback on the PAC12 tattoos, bumper stickers, clothing, etc.
So - as soon as you start seeing BIG12 tattoos, bumper stickers, clothing, etc. - in which the BIG12 logo is bigger and more prominent than the BYU logo - feel free to get back to me. I'm not saying it would never happen - it could.
But most of what OP is talking about either didn't happen (making fun of Ute fans for cheering for conference mates) or hasn't happened yet (dually logoed tattoos, bumper stickers, clothing, etc., where the BIG12 is more prominent than the BYU).