Most of the animosity towards Texas prior to the SEC announcement was just the typical dislike of the biggest, wealthiest school that exists in every conference. Iowa fans loathe Ohio State, even though that isn't a historic rivalry, and they only play 2-3 times a decade. They're the big dog in that league, and ergo receive that ire.
Since then, it's mostly the "we aren't good enough for you? Well, fuck you, then" anger at rejection form of animosity. Any animosity I've tossed at Texas was 100% of this variety.
All of this is really basic/typical human behavior and shouldn't be surprising to anyone.
I don't think the LHN really has anything to do with it. It's just an easy scapegoat. The schools that left previously left because they were either getting a pay raise, or thought that the league was going to blow up and didn't want to be left without a life raft. I think Nebraska and Aggy were most jealous of Texas's rise in the Aughts and needed some more concrete excuse. I