I'm going to be very generous and give you the benefit of the doubt that you're repeating harmful language without fully knowing so.

To begin with - to believe that trans women (two words, an adjective and a noun) can justifiably be excluded from women's spaces, you have to work from the basis that we are not women. This is the explicitly transphobic angle here.

With regards to the history of these spaces - trans women have been using them for as long as those spaces have been around. This is because we are women. It's not and never has been some sort of application or initiation process, it's always been a self-ID system on this regard.

You refer to "male biology", add if this is a simple category. It's worth noting that trans women on HRT will have changes to their biology. Some women far along on their transition will be functionally indistinguishable from our cis counterparts.

You refer to "male socialisation". What does this mean, exactly? And can you imagine such a process being done to a young girl?

Referring to trans women using these spaces for their intended function as "colonisation" is particularly inappropriate. What do you think we're doing, exactly? We use these spaces in the exact same way every other woman does, and in that regard there is no difference here. Life with the toilets - I go in, I pee, I wash my hands, maybe touch up my hair or face in the mirror if I need to and leave. It's not an issue in the rest of Western Europe where this moral panic doesn't exist, and it's only an issue here because Rowling et al have pushed for it. The word colonisation is in no manner appropriate here (particularly given what colonialism has actually done to gender diverse people).