On intersectionality. It is not really just a 'thing' - your post sounds dismissive to me. I might be wrong. But can you tell me more about how it is used to advance the campaign for TWAW?
Yes, I could feel I was being dismissive as I wrote that, but my charity has been depleted somewhat over the last few years.
I'm dismissive of it because while a I can see why it is a valid viewpoint to think about as one part of an academic framework, when it hits the real world, it goes bad, like post-modernism does. It's like a virus escaping the lab.
When you get down to it, it boils down to one of two things:
a) applied correctly, it's just saying "someone can be more than one thing at once", which doesn't seem like a very deep concept;
b) applied incorrectly - as it seems to be a lot now - it's "count how many things apply to you, add them up/net them off, and compare totals". So you've just gone back to a single axis. And then you decide to consciously treat people worse/better based on the total. 
So it's either not that deep, or it leads to dumb thinking and bad behaviour. The upside does not outweigh the downside. And people tend towards (b) just because (a) is so obvious - it's an attempt to "make more of it".
But that wasn't really my point - my real point was that no matter how much you value the concept, it makes no sense for "sex" to not be the one of the most significant axes.
The only other axis I can think of as underplayed is "wealth" (or "family wealth"), which is generally even more important than "sex" for most purposes.
And even if, as some point out, and it's true, that "perceived sex" (or race, or whatever) is what matters, rather than "actual sex", then, still, neither "gender identity" nor "gender presentation" are "perceived sex". Very few trans people are truly perceived as the opposite sex - especially males. Females can pass more due to the effects of testosterone - it's not symmetrical.
But now you just can't say to someone "no, you clearly aren't being treated like a woman, because everyone can tell you're male, and everyone is walking on eggshells around you - so no way are you in the same position on the 'gender' axis".
You have to pretend they're treated like women. (And the fact that you expected to pretend for them is an example of how they're not treated like women. It's paradoxical.)
Sometimes this is almost comical - it's been repeatedly observed how James O'Brian (UK radio host) speaks very brusquely and dismissively to real women callers and yet fawns over transwomen callers...
A realistic set of intersectionality axes up would certainly incorporate being gender non-conforming into a transwoman's "male+straight". GNC people - males in particular - are looked at a little askance.
But I believe the current view is that they're the most oppressed ever - even more than women - by flipping the "male+straight" to "female+lesbian" and adding the "trans". But that doesn't match societal or biological reality. You're feeding the wrong inputs into the algorithm.
GNCcentric and others have talked about how various LGBTQ communities use this to basically shit on transmen - telling them to "know their place" because of their male privilege and defer to transwomen. So now you're at a double whammy - doing the bad thing of deliberately mistreating people via "intersectionality (b)" but with incorrect totals on top, so your mistreating the wrong people.