I'm not sure what you mean by "places of public accommodation," but a number of people run businesses out of their own homes and, in the course of doing so, deal with the public. Some of the more common ones are cake decorating, hair styling and massage therapy. My niece will be getting her massage certification at the end of March and she wants to do massages at her apartment after she finishes her full-time job (warden). She's already cleared her preliminary license through the City, and eventually she wants to build up a big enough clientele that she can quit her job as a warden, which she really doesn't like.
She has mentioned not wanting to take on male clients until she gets enough money to open her own place, so, from what I understand, she's just going to be offering massages to women as long as she only has her apartment.
While the law may state that she can't turn a client down (based on his sex) if she's offering services to other paying clients, I think there should be an exception. She's simply not comfortable having scantily dressed men alone with her in her apartment. Her goal is to open a larger studio with yoga and couple other things, but she can't do that until she saves up the money. Plus, she doesn't want any hint of impropriety.
I think that's fair. But, if I understand the law correctly, it might not be legal.