Not to discount the trans readings of The Matrix or anything, but I honestly think it's quite reductive to sum the whole thing up as "it's about being trans."
I think the material the Wachowskis were heavily inspired by certainly spoke to them on a level even they may not have fully understood at the time and one can certainly see how a pair of very creative and talented "eggs" would find those sorts of themes around identity, self-image, and self-realization extremely compelling.
But The Matrix is not uniquely "trans" because of that. Those themes are deeply relatable to trans people, yes - and there's not a doubt in my mind that relatability was one of the driving forces for them to make the film - but they're also relatable to so many other people for so many other reasons. That's one of the great things about choosing to portray your ideas thematically rather than literally, the scope is so much greater. And there's plenty of stuff in the movie that simply doesn't parse from a trans reading no matter how you look at it - it's one element of a lovely tapestry, one of the colors of thread you can see woven in.
I think this plays into a larger problem I've noticed, where anything a trans creative does is often times read exclusively through the lens of the trans experience. When a trans person is so so much more than "just trans" and I honestly think it's a little insulting to read their work as just about gender.
The Wachowskis loaded up The Matrix with so many pop philosophy concepts and crazy ideas (don't even get me started on the sequels, which I will defend to the death) and personally I'd feel a little insulted if I did all that work and someone was like "well because you're [identity] this is just about [identity.]"
Again not to say that's not a part of it but wow you're leaving a lot on the table if your reading begins and ends there.
I guess really my point is that we need better media literacy and for people to realize art can be about multiple things. I think most people understand that but a concerning amount of people seem not to and will rebut any critique focusing on other elements of something like The Matrix with a blunt "actually it's about being trans."