It is utterly exhausting repeating what seems to me very simple. It is undeniable that sex offenders are muddying the waters for transpeople, but equally that this is not the fault of transpeople.
The question is, who should sort it out? Should women stop moaning and risk having sex offenders in the spaces where they are vulnerable, or should men (or call them 'male-bodied people' if you prefer) find a way of accommodating the wishes of those of their number who are innocent in all this, whilst protecting women from the guilty?
There is a third way, which is to ask transpeople to recognise that this is what they are, and accept that in order to live as transpeople they need to recognise the fact that male-bodied people in women's spaces do pose a risk, and have the decency and humility to respect the wishes of the women they want to accept them into our number. It's not going to have a massive impact, surely? Places where women are unclothed or less able to escape, and situations where strength gives male bodies an advantage aren't so commonplace as to make a huge difference if men are asked to stay away. If this is in return for acceptance as transpeople in all other aspects, surely it's a good tradeoff, even apart from the expectation that people who believe that they are women would understand.