As long as it’s not a protected class. For instance, I was once a hiring manager and everyone I was talking to was shocked when I said I would rather hire someone older and more stable. They thought I was opening them up to a lawsuit. Being under 40 is not a protected class. Being over 40 is.

I also told the recruiter that I wasn’t going to hire a guy because he smelled like cigarette smoke, I would be working closely with him and it bothered my asthma. Cigarette smoking is not protected in some states - including mine.

My understanding is that the "shared housing" clause is still only applying to landlords, not individuals seeking a roommate.

So if you're the Catholic Church running a women's boarding house on the upper east side of Manhattan, you are allowed to advertise to (and rent to) only women, but you can't restrict it further to only Catholic women.