Are there even statutory or regulatory codes that give TABC the authority to consider or review a private businesses' internal rule about vaccines as a factor in whether or not an establishment can hold a liquor license? Most state agencies are terrified of taking any action that isn't explicitly authorized by statute--not just in terms of the general subject area for which they are authorized to regulate, but even in the scope of authority they have to request or consider additional information not directly related to the issuance or enforcement of permits, etc.
It would be like the Railroad Commission denying a drilling permit because RRC found out the operator was catching redfish that didn't pass the size limit.
Edit holy shit, from that article I should have read before posting:
"To ensure Texas businesses follow that rule, “each appropriate state agency” — in Launderette and Fresa’s case, the TABC — “will ensure businesses in this state comply,” according to the bill. These agencies can “require compliance [...] as a condition for a license, permit, or other state authorization necessary for conducting business in this state.” "
Looking forward to the state asking Exxon, Chevron, etc. about their vaccination policies for every permit and registration they apply for. After all, if you're checking up on the little mom and pop restaurants, it's only fair to ask the big guys, right?