There are also (typically) greater legal and institutional barriers keeping transmen out of male space, at least when it really counts.

Laws typically let transwomen keep male advantages while gaining women's compensatory advantages, but not vice versa. Sometimes the law tries for structural equality, but not equality of outcome - for example, most if not all EU countries have carve-outs so that transmen cannot demand to be treated as male when it comes to religious orders and roles. In theory, this can be equal - no transmen in a monastery, no transwomen in a convent - but what major religion assigns powerful positions to women? In practice, it means transmen (and women) can't be priests, bishops, pope, orthodox rabbis, imams, etc. - but legally, transwomen still can.

There's also primogeniture - where there are systems that grant inheritance rights based on sex and age rather than just age, transmen don't take their place in the inheritance order for titles or lands or money, and transwomen don't lose theirs.

In the UK, there have been complaints since the nineties - which I've rarely seen talked about openly and never covered in the press - that any transwoman with a "Gender Recognition Certificate" can be assigned to a woman's prison, but transmen with GRCs are not even considered for the male estate unless they have had phalloplasty.