My guess would be because an LTC (like a driver license) clearly indicates if you are a state resident whereas a UT student ID does not?
The student IDs can certainly be modified to contain that info, but until they do it makes sense that they aren't a strong enough ID for voting.
And of course, it's a state run university. If the state really cared about making voting accessible to people with valid IDs, they would update the UT IDs to meet whatever requirements they deemed necessary. They've had 6 years. Why haven't they done it? Students actively want the change.
On the other hand, I'm pretty sure that a Texas Handgun License requires citizenship.
https://www.dps.texas.gov/rsd/ltc/faqs/index.htm
> 12. Can non-US citizens obtain a License to Carry a Handgun? > Yes. Subject to the requirements of federal firearms law, and if not otherwise ineligible, resident aliens and certain nonimmigrant aliens who are lawfully present in the United States may obtain the license.
Amusing how quickly the requirements grew.
Ref: https://www.ncsl.org/research/elections-and-campaigns/same-d...
[1] https://www.campusvoteproject.org/student-id-as-voter-id
I see that 10 states will accept student ID, but there are restrictions on which IDs. For example, it has to have your signature on the card, etc.
As for your question, supporting or not supporting voter ID is less about how difficult the IDs are to get, but rather that it is creating a requirement that makes both the act of voting and the preparation for voting much more time intensive. And this is all to solve a problem, voter fraud, that nobody has any evidence occurs at any appreciable volume.
But I'll just say, if a system existed where I could get a photo ID with no fees and no wait times, and I could do it on election day, then I'd be much more willing to support voter ID laws.