I still do not think that UT Austin will care. I also still think that providing mental health services to any teenagers, whether LGBT or not, is a good activity. Mental health is something that is probably not given as much attention as it should in our society.
Remember that the admissions staff at UT Austin are not the same thing and not the same people compared to either our current federal government or the current Texas government.
I think that you are fine, and should not worry about it.