And if there's anything decades old social science research has taught me, it's the Overton Window: https://en.wikipedia.org/wiki/Overton_window
Debate is a cornerstone of democracy - to take the climate change example, anyone should be able to question it, and the evidence for it should be what persuades the majority of people, leading to a decision. In these cases, debate is a very effective mechanism. Unfortunately, people don't tend to engage and debate properly.
A good, reasonably relevant read (5 min) is Isaac Asimov's A Cult Of Ignorance, which I think goes some way to explaining the lack of engagement with debating.
NB: I do not know what the scientific consensus is on cognitive differences between men and women.
Edit: And I didn't ask the OP if they are skeptical of climate change. I merely asked if they would be in favour of letting those that are skeptical express their opinion.
No, it is possible to defend every point imaginable. Look up "Hempel's ravens". It is trivial to generate evidence supporting or opposing any claim you like.
I'd love to have similar conversations about how nature and nurture affect outcomes, including how race and sex tendencies are or are not swamped by a lifetime of socialization, but our society has absolutely no way to do so without hurting a lot of people. We have other good work to do, so we can defer those conversations—maybe past my lifetime. Maybe try having them in smaller settings, with a framework of trust and love?