I don't know where you get that idea from. The gender-critical 'crowd' is extremely disparate and includes lots of people of both sexes with plenty of experience of marches, protest groups and the like. In the UK they are more likely to be left-wing than right-wing, although there are people from all political parties perturbed by the flight from reason that gender ideology represents, and the many practical problems resulting from that, many of which are causing long-term harm to children, women and other vulnerable groups.
Helen Steel is gender critical. Ask her what she thinks about the police.
Ask the women who found themselves stuck on the stairs in the Jam Jar in Bristol trying to get to a meeting, with the police outside refusing to intervene. Ask the women who tried to hold a meeting in Manchester who couldn't gather by Mrs Pankhurst's statue, because trans rights activists were blocking the way. Once again, police refused to intervene. Ask the various women who've been arrested and interviewed under caution after complaints from trans rights activists - Marion Millar, Kellie-Jay Keen, Kate Scottow, Jennifer Swayne all come to mind. Ask those who've found that they have non-crime hate incidents recorded against their names by the police, which the police hadn't bothered even to tell them about, never mind try and find out if anything worth recording had even happened - Sarah Phillimore and Harry Miller, for example.
There's been plenty of discussion about the deep-seated misogyny in the police on this board over the years. The Met officers who've been sacked or imprisoned in recent months could fill dozens of threads single-handedly.