There is no way of stopping someone who decides to do so from harnessing their ideology to yours by them arguing that you two are for the same things, when it blatantly is a lie. No way.
JK Rowling answered this quite brilliantly on Twitter, but got thousands of trans activists arguing that she and Putin clearly share their ideologies.
The same problem comes up when left-wing women protesting their erasure are force-harnessed together with right-wing causes. That the two camps have opposite reasons for wanting female biological sex not to be erased is ignored. (Conservatives want to keep the female sex subordinate, feminists want equality of the sexes, but both causes need to be able to define what 'women' mean.)
Then there is the other kind of forced-harnessing-together: Trans activists link their cause with anti-racism or disability rights, arguing that anyone opposed to the erasure of women is also guilty of racism and ableism. That is simply not true, but can be quite effective.
All the things I have mentioned are dishonest forms of debating when someone cannot actually address the real questions.
And Putin is a misogynist who wants regressive sex roles in Russia to stay forever. In that particular aspect he actually has a little more in common with those who define 'women' by clothing of by femininity than he has with JK Rowling.