No true Scotsman there. It is true that people who say that aren't for equality, but they still call themselves feminists and feminists still welcome them as their own. That is the point, feminism as a movement isn't really for equality, they say they are but they aren't really or else those wouldn't get accepted in the movement. Your movement gets colored by the rotten apples in it, just like mens right has a lot of bad apples so do feminism, and what those bad apples do will also get attributed to feminism even if you think it shouldn't.
> There's some truth to this, but it's also omitting something that's extremely important (and therefore changes the entire tone of this argument): we should also encourage men to handle that burden rather than totally drop the ball and shame men who dare to cry. It's not men vs. women. It's men and women together. That's what feminism is.
You say it is men and women together here, but why do they just blame men for this? Most men live with a woman just as most women live with a man. The woman is his closest link, she is what affects him the most, if she practices toxic masculinity then there isn't much he can do. And as most men have experienced women like that they will teach their kids and each other that they have to be stoic and not cry, since otherwise women will not see them as a man. Sure, there are women out there who can accept a man who cries and do it well. But, as long as there are lots of toxic women out there who refuses to let a man cry there isn't much men can do, the "men don't cry" will live on as long as such women exists. And feminism doesn't try to do anything at all about those women.