Can a man be in a Women's only spa area wth nudity?

I'm 33, lesbian, and my gf is 37. We live in NYC and recently visited Spa Castle in queens.Part of the hot tubs and pools are gender separated and in the women only area, nudity is required. No suits allowed in the pools. Gf and I went naked and got in- while there we saw a woman sitting next to what looked like a man. They stayed under the water, talking for a long time.This area is not easy to get into and we assumed ok trans maybe? We were cool with it for the most part.Then this guy stood up and was wearing a speedo in the pool. Wait a second, that's just a dude! Or was it?This sparked a convo about gender and spaces and sexual orientation.Were we as lesbians welcome there? Kids were running around naked. We kept the PDA to a zero and of course don't stare at others. We are bio gender female and identify that way.If he was a gay man in a Women's only area, is that ok?If he is trans and pre op and FEELS like a woman, is that ok?If he is a straight man in a naked women's bathing area, is that ok?Does gender conformity take priority over sexual identity when it comes to naked spa areas?Would love to know what people think!We talked about it a lot and saw all sides of the issue.