Heck, they even played Dixie at the U of T, and I know the Aggies played it. But that was some years ago.
No native Texan I knew considered themselves solely Southwesterners. We considered outselves Republic of Texas first, Southern second, Southwestern third. One would never disassociate oneself from being part of the South; thus being associated with Yankees which, in Texas, are anyone not priveleged enough to not be born and raised South of the Mason-Dixon line and East of New Mexico.
Maybe it depends upon which part of Texas one was raised? I guess Kennebunkport was the Southwestern part of TX and that hotel for tax purposes in Houston was too “new” to be Southern.
Texas A&M is getting a Political Correctness and Yankification Makeover by the Powers That Be. A few years ago, a member of the Corps who had a small Confederate battleflag sticker on his footlocker was told to remove it. He demurred, and the Yankeefying commandant, a retired bird colonel in the Union Army, told him to remove it or be expelled from the Corps. I don't know if they'd have tossed the kid from A&M as well, but the sentiment seems to be that the Powers would rather that all those East Texas white kids stay home, back in the woods, and learn to fix air conditioners and peddle doublewide tornado-magnets trailers, and save the spaces at A&M for more-deserving applicants of the politically correct social backgrounds.