Billy's "wrong side of the table" argument is no different than the argument of those who try to silence any legitimate protest against Israeli policy by lumping all criticism of Israel and all concern for the rights and wellbeing of Palestinians, as having sympathies with Nazis and antisemites. What would he say to someone who pointed out he's on the same side of the table as neo Nazi, because neither of them are likely to be fans of Netenyahu?
Some people have reasoned, evidence-based concerns about an ideology that defines womanhood away from its material, biological, objectively quantifiable characteristics. These people oppose policies based on that ideology, because such policies recklessly cause risk, harm, and disadvantage to women, by depriving them of single-sex spaces, and to children by subjecting them to experimental and irreversible medical interventions including sterilisation and the prevention of maturity.
Other people think men and women should live according to strict gender roles, that lipstick and high heels and helplessness are all inherent parts of femaleness, that men and only men should be big and strong and never cry, and that homosexuality is sinful and icky and shouldn't be allowed.
These are not the same people. Anyone who still thinks they are, must be an idiot.