You should certainly report hate speech. These threads are well moderated.
This debate does really come down to body parts - it's the fact that men and women have different bodies that leads to women's need for sex based rights. Access to contraception, maternity rights and legislation that protects women from being dominated by men is the difference between now and the past and this country and places like Afghanistan. Many of us have seen these rights be created in our life time. We know they can't be taken for granted. You can't protect a class of people you can't describe.
Re: perverts, the question is not really whether trans women are perverts, but whether polices have allowed men to take advantage of loose or absent definitions of 'trans' and 'women'. The almost weekly stories of court cases involving sex based crimes by men who claim a (sometimes very recent) trans identity suggest that it has.
Is the TRA movement dangerous? Well somebody carried the signs at the demonstration and defaced the statue, and apparently nobody stopped them, so I think we can draw our own conclusions.