I think it’s a bit of a stretch to claim a religious exception. And that’s because it wouldn’t be unreasonable for the bar to think that your beliefs would harm another person’s health.
(I’m not saying that the bar would be correct in thinking that. I’m just saying that the bar would not be unreasonable in thinking it.)
As conservatives, we hold property rights in high esteem. So I’m on the side of the bar in this one.
The bar owner holds a place of Public Accomodation. As such he cannot discriminate.
What he is doing is setting himself up for one hell of a lawsuit.