Whether he goes to the gym to get physically fit or does so through a different means that has nothing to do with a gym, she doesn’t care all that much.
Whether that reason has to do with a history of alcohol abuse, or a disdain for the taste of alcohol on your taste buds, there is nothing wrong with you refusing to drink alcohol.
Although you are worried that every girl your age wants to date a guy who drinks alcohol, as it is normally at the center of social venues, this trepidation is misguided.
There are plenty of girls who are perfectly fine with you refusing to drink alcohol.