The Eyes of Texas was parodying a Texas president who constantly paraphrased Robert E. Lee saying, "The eyes of the South are upon you!". It definitely originally referred to the Confederacy.
Here we have a symptom of the problem. White people can't tell black people that they're being offended by something that shouldn't offend them. If you've heard the term "white privilege", this is an excellent example. The origin of the song might not offend white people, but the black students are saying it does offend them.
The song might not need to go. Maybe, after discussion and acknowledgement, an understanding can be achieved. I think that understanding is extremely unlikely if white people start by dismissing the concern out of hand.
From afar, I have watched this unfold. I was not aware of any racist history or undertones to "Eyes of Texas" before this blew up. But I was not aware of any racist history to "I've Been Workin' on the Railroad" either, and that definitely has a racist history, as the words to the verses were originally written in 1894, at Princeton, of all places, in "Negro dialect." Very, very crude Negro dialect.
OTOH, the tune of the verses comes from the
Poet and Peasant overture, by Franz von Suppé. "Someone's in the kitchen with Dinah" and "Dinah won't you blow your horn" come from two different sources, one from the 1840s and one from the 1940s.
I also didn't know that "Eyes of Texas" was an allusion to R.E. Lee and "eyes of the South" (I would actually guess it was "eyes of Virginia") either. But that makes sense.
I was aware of the "cowboy minstrel show" history of the UT marching band uniforms, however. Were I an aggrieved black UT student/alum, those outfits would have been my first targets.
