I've spent the last 4 months regularing Tumblr over reddit (after primarily regularing Reddit for 5 years), the ultimate "cis white straight males are the devil" website according to most places, and have yet to see anyone actually agreeing with anything like "man spreading". If anything, I've seen that kind of mindset criticized more than sympathized.
I also haven't seen anyone saying "men react to periods like vampires to sun" in anything other than a venting/joking way. The vast majority of women know not all men view periods that way, but enough do (I mean, have you talked with a lot of guys in their late teens to mid twenties outside your personal social circle? A lot of them certainly are the "lol periods are gross" kind of person) that it's annoying to them.
I also find it hard to believe you haven't seen anything venting or joking about white, cis, or straight people in a similar tone.
No one is trying to downplay men's struggles. Anytime I've seen anything close to that is when it's in the context of a man bringing up men's struggles in a conversation about women's struggles, effectively trying to make the discussion about them. The solution would be to begin a separate discussion, but anytime I've seen that happen, a good amount of the people involved just end up bashing feminism.
Most of the feminists I've come in contact with have said something along the lines of being totally down for the men's rights movement, if it wasn't so primarily fixated on bashing feminism. Some even question the need for a separate movement for it, since a lot of what MRA's claim to be about are also things feminism strives for.
Very few feminists I've met seem to think men shouldn't be talking about men's rights, they just don't think it should be happening in discussions about women's rights. If anything, the more prevelant mindset I've seen is questioning why more men aren't talking about men's rights like women are talking about women's rights. I've even seen criticisms that a major problem is the lack of intersectionality. Feminists often talk about the struggles of women of color (and again, women of color would appreciate it if white women didn't talk over them, just like women would appreciate it if men didn't talk over them in regards to their issues, the difference being women are more likely to understand what that means and how not to do it) or queer women (same thing), but any time I've tried to dive into a men's rights circle, it's just general bickering and complaining about feminism, with very little actual discussion happening about men's rights, much less men of color's rights or queer men's rights.