What about females that want to self ID as males?
Do they get the same recognition/rights etc as the males self IDing as females?
Is this a serious question? I'm going to make the assumption that it is, because realising that trans-right activism was pretty much entirely focused on TIMs was the first step for me on the road from 'transwomen are women' mantra-repeating liberal to peak trans. And once you peak trans, no one ever ever goes back (and that ought to tell you something too). So actually thank you for asking the question, because the more this gets out there, the more debate there is, the more people peak trans.
First off ask yourself this: trans-identified men make the news for sporting achievements, achieving political positions, etc. Meanwhile, what do trans-identified women make the news for?
And as for the same recognition/rights, look at primogeniture. A TIM who legally changes his sex to female will be unaffected and still be able to inherit. The fact that this is an exception (and that no trans-activists seem to give a shit about it being an exception) should tell you exactly where the priorities really lie: with men, trans-identified or not.
And as for TIFs being able to access male spaces legally, that's missing the point. Biological females simply do not present the same danger to men that men do to women -- 98% of sexual offences are committed by men. Men don't have to worry about their spaces being taken over by women, because women do not present the same threat.
Aggressive men have no issues with shouting women down, silencing them, threatening them with rape and violence. Funny that, since that's pretty much the behaviour of many trans-activists. What does that tell you?