I'm in biomedicine. In my field we have to know the difference between male and female, for some of my clinical colleagues it's the difference between patients living or dying. Nobody has a problem with biological sex in a medical/scientific context. Something that I find odd is that some of my colleagues still believe in gender 'outside work' and will insist that for anybody who says they're trans, we must all pretend they're the sex they want to be instead of the sex they are. These are people who think logically, understand complex biology and do medical research where the division between the sexes is integral to getting the research right, but they seem to have a huge blinker on that divides scientific and medical reality from the 'gender world' they inhabit the minute this subject comes up.
Another issue is that there's a lot of scientific and medical lack of understanding in the general population in my experience, including among people who may be highly educated in other areas. I think we have access to a lot of medical and scientific information online, in documentaries and in books. There's a lot of misinformation out there too and some of it sounds plausible, or is spun to sound plausible, unless you know a subject quite well. If it's not an area you know and you listen to somebody who sets themself up as an expert then you could easily be mislead. My knowledge of history is minimal so if somebody who said they'd studied history told me some rubbish about the life of King George I, complete with made up events and dates, I wouldn't spot anything wrong unless I wrote it down and checked (assuming I could recognise a reliable source to check), or unless it was totally outlandish.
There's also an odd disconnect between people who will believe and promote somebody who knows little about the subject talking rubbish about biology (e.g. a philosopher who claims male and female testosterone levels overlap) but are keen on claiming they want to follow the science on something like Covid. I suppose it's the difference between believing anything that supports an ideology you like which you see as not having any cost to yourself (and not caring about the cost to others) and believing in reality when there's a risk of your own death if you don't.
I suppose a result of this is the people who think they know about science, even when what they believe is total rubbish, and will assert that even when talking to people who really know what they're talking about, like that student trying to tell Robert Winston he's wrong about biology. What I struggle to understand is the fact that they see an eminent biologist, saying something about his field of expertise, and they don't think 'hang on, maybe he's right'.