I think a lot of the problems around this debate is that it's being driven by a tremendous sense of urgency due to the medical treatment of children (one side saying "act now! quick! suicide risk!" and the other side saying "stop! immediately! these treatments are dangerous!") and the legislation changes which effect women but which are being decided without consulting us. Thanks to #NoDebate this is also largely happening in echo chambers. On Mumsnet the feminist boards are largely just used by like minded people now, and the TRAs mostly seem to use Twitter and have blocked any opposing opinions. The problem with #NoDebate is that you can't actually stop people from talking about stuff, you can only stop them talking to you about it. That immediately stops any chance of finding a middle ground and forces opinions to become more polarised.
Within the radfem community you'll find a wide diversity of views - everything from people who personally don't have a problem with mixed sex spaces but are advocating on behalf of those who do, people who think that it's OK for some spaces to be mixed by not others, people who want a third space on all occasions, people who are fine with the current GRA but oppose self ID, and people who find the whole concept of being transgender so dangerous and offensive that they want to repeal the GRA entirely. There is no consensus on this stuff between radfems. The only general consensus is that we want the rights of women to be held equal to the rights of trans people, that we don't believe this is currently the case, and that we want to have a public discussion around that.
Amongst the trans community you get equally diverse opinions. Some transpeople believe that sex and gender are separate and that although they are and always will be the sex they were born they would like legal and social recognition as if they were the opposite sex. Some believe that sex and gender are the same and therefore if you have a female gender you must also be, literally, of the female sex. Some believe that gender is a social construct which basically means sex role stereotype, but believe that these stereotypes are the ultimate markers of male/ female, not the biology that they commonly associate with. Some believe that gender is an innate and essential thing, but ultimately non physical thing, kind of like a soul. Some believe that gender is biologically determined and manifests physically and that we will one day be able to test for it. Some believe that to be transgender you must have gender dysphoria, others disagree. There are many many more belies and opinions about this out there. So a very wide range of opinions on what is meant by the words "gender", "sex", and how these terms intersect.
And I personally am happy to have an ongoing philosophical debate over the meaning of these words, just as I'm happy to debate with theists over their ideas about a soul or an afterlife. But I feel very strongly that until there is some kind of agreed definition and coherent narrative around these ideas we shouldn't be basing legislation and medical policy on them, especially as that medical policy is being written by groups with a financial interest and used on children.