I disagree with the original premise of this thread- that most spaces aren't GC. I think the majority of people in the UK don't consider themselves gender critical but their views align with key aspects of GC thinking.
Most people aren't interested in trans issues. Not because they are transphobic or trans allies, but because they know trans people are people and don't understand the fuss being made about gender expression. In the UK today, even conservative people tend not to get excited about gender non conformity when it comes to gender expression. Most people are pretty liberal when it comes to who wears what and what names people choose. Most people are fine with this.
The majority also do a mental translation exercise when people discuss trans woman/men. You can see their brains whirring and trying to remember if the word transwomen means a woman wanting to be a man or a man wanting to be a woman. Those who have 'less fucks to give' talk this through aloud.
The majority (who tend to think they don't care about trans issues), tend to have a view about preserving single sex provision where it's needed.
These views are prevalent because they are formed from life experiences (not ideology, post modernism or feminism). People know that there are 2sexes, they know that what people wear, how they style their hair, or how they think about themselves, doesn't change their sex. Most people don't think this is worthy of any headspace.
This is why TRAs won't give up their approach of trying to bring about their wishes by stealth and when that fails by bullying and intimidation.
They won't win people over through critical thinking/reasoning.
Ultimately they know they will fail (which fuels the anger). The stealth changes come to light and people push back and they are undone. The bullying and intimidation only controls those who are trying to appease. It won't work on 'the man on the Clapham omnibus' such as the angry dad who finds out there is a male in his daughter's changing room.