The OP poll raises a good point because I think everyone's instinct is "of course he can refuse." BUT then we get into the absolutes of platitudes to rationalize about it.
The topic of discrimination can get lost in such absolutes leading to freedom being replaced with authoritarianism. Generally, most people will be decent and normal if they are treated decently and nicely.
When we decided to make a spontaneous drive to Key West, not any real timing or destination schedule we didn't make reservations not knowing when we would end or where. However, it was a holiday weekend and as we drove the long length of the Keys every hotel was full. Finally, in Key West after midnight we had to get a very expensive suite at the Mariott. We were going to thus spend the day in Key West, but drive out that night into Miami for a room.
But as we went around Key West on a rented scooter, my wife said she wanted to ask if they had a room at a very colorful, quaint little hotel entirely enclosed by fences and plants. She quickly came out informing they had a room. However, when I went back in with her the owner started hedging not sure how to say what she needed to. Her and I both understood. We hadn't noticed the coded words on the sign. Or maybe I hadn't and my wife had and that caused her to think they might have a room available? Because of the qualifiers, it had vacancies where no other hotel did.
This was a hotel specifically for women - and more specifically lesbian women. More along the lines of a private club, though open to all lesbians. My wife asked to speak to her privately and 10 minutes later we had a room with an exit straight out to the sidewalk, the only request that I not go in the private pool area as the women like to go naked there. However we were welcomed to use the tiny dining room as long as we didn't go thru the pool area to get to it.
Does that hotel "discriminate?" Absolutely. The owner discriminates on both sex and sexual orientation. AND I HAVE ABSOLUTELY NO PROBLEM WITH THAT. I see no problem with a lesbian woman wanting to set up basically a mini nudist camp hotel for lesbians. I would have no problem with someone doing so for straight couples either. I think women - straight or gay - certain can have their own naked pool area and it would be going overboard to declare it illegal and the woman lose her hotel in a discrimination lawsuit.
I do not like discrimination. But I also do not like the absolutism many want to apply to it.
PS edit... To those who response "but what if everyone..." my response is then we'd deal with the problem. "But what if everyone..." is rarely a persuasive argument to me. Sometimes it comes down to are we all going to equally have no individual rights or unequally all free to be ourselves?