Since "Private companies arent the government" does that mean I can refuse service to anyone wearing Hijab?

I thought to myself today that when people claim they are "against discrimination" they are really only against selective forms of discrimination. I mean, look at that Wonder Woman movie screening that excluded men. That's a clear instance of discrimination but it doesn't seem like too many people care about that.

Even when Alex Jones got kicked off YouTube for his speech, there were many people claiming that "Private companies are not the government so his rights weren't in danger from the state."

To be consistent with that argument, if I would be owning a fitness gym, I wouldn't be obligated to throw everyone out of the pool for an hour just because some Muslim women are convinced their imaginary friend is going to strike them down just because they have the audacity to bathe with other men. And since I'm not the government, just a private business owner, I wouldn't be infringing on their rights in any way.

And once I thought about this, I recognized that I wouldn't even need to service them if they came to my gym wearing a Hijab. It's not a lot different from instituting a dress code that all customers are required to follow. And since Hijabs would break that dress code, there's no reason to cater to someone's personal religious beliefs. Its no different than kicking someone out for going shirtless in your establishment.

I really don't see how any of this makes me a bigot.