As others have said, just having a button doesn't mean people will automatically gender you the way you want. People aren't used to hunting around for a button to figure out what pronouns, and nouns, and even adjectives to use when talking about you.
It gets even worse if they see it one day and train themselves to do it one way, only to have to retrain themselves the next day.
Me, I have enough trouble using the correct gendered words even in cis society. (I've found myself saying "her father" when I meant "his mother.") I think I'd be hopelessly lost if I had to deal with someone whose gender changed daily.
And if you were talking about the person when zie wasn't around and you hadn't seen that day's button, how would you know which gender to use?
I think this is a recipe for getting misgendered. (Of course, if that's what floats your boat....)