I love cosplay and really enjoy cosplaying in spaces where it is part of the experience, like broadwaycon.
My personal feelings is that it's not appropriate to go all out cosplay to a broadway show, the same way it is not appropriate to go in pajamas. Beyond that, I would worry that people involved with the show would think I was creepy obsessive and that's a stress they don't need to deal with. Now, not all people agree with me and lots of people who aren't creepy obsessive cosplay to shows. I have a friend who has. But I am not personally comfortable with it and said if they were cosplaying that was fine but I'd go see a different show.
My preference is the 'broadwaybounding' type of outfit that fits the show without directly copying it. I love spending a bunch of time mulling over the colour palettes, textures, themes of the show and putting something together that reflects that. For Comet my partner and I wore bold reds, elaborate rhinestone jewelry, a fancy hat (removed before show started). For Hadestown I wore a brick red skirt in a 30s cut.
It's fun and fitting without being over the top, so that's my choice, but I don't think it's a sin if you cosplay or anything.