It was written by a guy who did minstrel shows and he advertised it at a minstrel show. But I don't think it was written for the show, was part of the show, or was in actuality was "a minstrel song". Its missing the characteristics of minstrel songs that make them so offensive, such as the played up African American dialect in the lyrics as well as the mocking tone directed at black people. It was written with a different purpose in mind and has very different content from abhorrent minstrel songs.
Compare this
When I was young I us'd to waitOn Massa and hand him de plate;Pass down de bottle when he git dry,And bresh away de blue tail fly. Jim crack corn I don't care, Jim crack corn I don't care, Jim crack corn I don't care, Ole Massa gone away.
To this
The Eyes of Texas are upon you,All the livelong day.The Eyes of Texas are upon you,You cannot get away.Do not think you can escape themAt night or early in the morn --The Eyes of Texas are upon youTil Gabriel blows his horn.
Do you get what I'm saying? If the meaning behind Eyes was anything remotely similar to the content of minstrel songs I would support its removal and replacement.
I'm not going to die on this hill but just giving my two cents.