But you are assuming that Brown Sugar would be on my submitted set list (which it would not). There are many songs that have been requested that I can't or won't play for whatever reason. I do not normally take requests, and if this offends you then I understand and accept your choice of going elsewhere. However, you do not have the right to force me to do a song no matter what the circumstance.
It highly depends on who you want your audience to be. If you said ahead of time you have the right to discern which songs you will play based on your morals (say you won't play a love song if it's between transgender people) then your listeners can chose for themselves if they want to listen to another song.
If, however, you don't give that sign then transgender consumers wouldn't automatically know your disapproval to playing the couple a wedding song. It would be taken as an insult because they didn't know otherwise until they asked.
While you can play whatever you want, legally (US), unless it's your business and you have some type of sign (songs chosen by owners discretion), it is disrimination. The customers aren't in the wrong because of their ignorance to who you want to play the song to.
That, and a sign saying you won't play Brown Sugar would be appropriate so the couple knows they can still have a song played but the owner made it clear what songs he will not play Regardless who asks.
Legally, discerning who listens to your music and which is more of an issue than whether you want to play one song over another. As long as your decision is well know upfront it sends a signal that it's not because of your choice in what you play but directed to not playing a song because of the consumer. In other words, it looks as if you are choosing not to play because of the customer not because of your morals of which song you want to play Regardless the listener.