I think the personal reference criterion will effectively gatekeep; women, transmen and born female people who identify as gender-fluid will all be neatly blocked out by that.
There are many people who are willing to go to all kinds of effort with pronouns at work, and other people who will go along with it at work because they feel obliged to do so. It doesn't automatically follow that they're willing to spend their free time with you, or that they want to transgress the social norms of their friendship group by bringing you along to a meet-up. For that kind of thing, you need to build very strong inter-personal relationships with people. At this point, we segue into my advice for incels, which runs along the lines of 'develop a sense of humour and a personality that extends beyond seeing other people as there to serve your needs'
Anyway, I could make a big noise about identifying as a man, but I'd have to commit to surgery and so on before any bloke would risk sacrificing his social credibility with his lodge to get me admitted. Calling myself David two days a week would absolutely not be enough.
However, this doesn't mean that they fwant to spend their free time with you