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One solution is to question their competence to speak on this subject, and assert the superiority of lived experience over purely theoretical knowledge.
Another solution is to weigh (their) rationality against ethics. Many purely rational policies have led to disasters and horrors. Eugenics, for example, is perfectly rational.
In my view, this is part of what feminism still brings to the table despite what people say and all the arguments inside the topic and outside about the topic. When its only men in there, they speak assertive and with authority, when these powerful spaces allow others in or they barge in, the communication hopefully changes the powerful man's point of view.
I say this because I was just reading this article a bit ago and really kinda makes sense of it. Its good to use hedging language, we just view it as weak. Thats often how science works, you cant always make strong claims unless you have high confidence in your findings and can rule out external factors
https://www.nytimes.com/2023/07/31/opinion/women-language-work.html
While I don't disagree with anything you said, I'm not sure how this answers the OP's question. At least without a little bit more elaboration on what assumptions you're making and why you're bringing up feminism specifically in this case.
Just to take a stab here though, I think you bring up feminism because more often than not men will discredit women because "women get emotional". And since the men in this situation aren't crying from whatever casually horrendous shit is being said in the name of "debate", that to them, they think they are just and unbiased and have a more unbiased opiniom than women. Which ignores how men will often react angrily to a woman who buts into their conversation and not even realize that anger is an emotion too.
Maybe you could prod them by asking them questions designed to highlight their unconscious biases? Assuming that they're not a malicious actor of course and actually genuinely trying to learn and expand their worldview.
I do think it's important to determine whether the person you're arguing with actually cares to grow and learn or if they're just trying to start fights with people and "win" arguments with comments that take a lot of nuance to address. In the cases where they don't care, don't waste your breath on arguing with someone who's sole purpose is to make you angry. They don't care about your nuanced answer.
I forget how the original phrase goes, but someone once said that these people use language as a toy to play with, while the reasonable person uses it to justify their actions.