In Texas the Costcos have a liquor store that does not require a membership. But so far as I can tell, the alcohol sold in the Costco-proper likely does require a membership. Perhaps the presence of the liquor store satisfies the legal requirement.
Related to this, Texas also has "blue laws" which ended in 1985 other than the parts covering automotive dealers and liquor stores. So in Texas, liquor stores cannot be open on Sundays (nor can car lots). This is another reason Costco may be incentivized to not sell liquor within the member-only part of the store separately from the other requirements from TABC, because they are open on Sundays.
Anyway, grocery stores will turn off the beer cooler lights on Sunday morning and put a note with the time they will be able to sell it.
It's annoying, but I deal with it because my local liquor store only has two employees, and the wife is behind the register 12 hours a day 6 days a week. Sunday is the only time she gets off.