There's a fair amount of crossover between MGTOW, the "Red Pill" lifestyle and PUA's so things I'll say will likely touch on all three.
(And yes, I fully appreciate the seeming irony of MGTOW... a group basically around "cutting themselves off" from women and certainly under no circumstances ever having sex with them... and PUA's... a group all about having sex... crossing over, but they certainly do. Both are basically reacting in different ways to the same stimulus; one divests themselves of what they dislike completely, the other pretends to be something else in a hope to "succeed"... using the term very loosely... at it. It's not even the weirdest crossover I'm going to mention).
As a general rule I try to separate ideas themselves from the people to speak (or even originated them). Someone can be the biggest... I generally try not to describe people in such ways but "arsehole" is probably the most accurate word... on the planet but that doesn't mean their ideas or wrong... or even if their specific idea is wrong that the general idea behind it is also incorrect. So whenever I watch, listen to or read about MGTOW I try to avoid basing my entire opinion on MGTOW on the fact that the people behind it invariably turn out to be... well, there's that word again, arsehole. And even doing that, even ignoring how toxic and malicious such people appear to be there's not a huge amount of value I can find in MGTOW.
Having already lumped MGTOW and PUA's together let us once again go to strange pair of bedfellows... if one considers the intellectual position behind extreme lesbian separatism and MGTOW there's no much to slide between them. Both, rightly or wrongly (and I'd say wrongly), see a world that is biased against their sex/gender (I use both to account for all positions within the movements) and have decided the best way to solve it is to take the whole "the personal is the political" to the extreme; if men/women are the cause of such great evil in the world then to prevent evil being done to you cut yourself off from men/women as much as possible. In fact the only real difference is that the lesbian separatists "decided" to become lesbians (as the name suggests) while the MGTOW crowd didn't "decide" to indulge in a little man love themselves... and instead tend to have... let's be polite and say "really, really stupid" views on homosexuality.
I have little sympathy with either position.
To break the golden rule and actually split the political and the personal, MGTOW's political position is basically taking their ball and going home. And that's it. They, rightly or wrongly (and again I'd say wrongly), see a world heavily and deliberately biased against men and so decide to try not to engage with that world. Great. If this was a movement with millions of members then it would still be a fairly stupid way of dealing with problems... when it's a movement of youtube videos and forum posts it's spectacularly ineffective. As much as our egos would like to imagine life as some John Galt fantasy where we all withdraw our labour and show how rubbish the world would be without us, that's not going to happen... whoever your nomination for the smartest/most important person in the world is, if they suddenly disappeared does anyone really think the world would fall apart? It becomes even more silly when you browse over anything the MTGOW crowd say and 3/4 of the time it's shouting at feminists. That's not so much "going your own way" as "going a bit down the hall and then constantly trying to get the last word in."
That said, there is at least some purity to a "screw it, I'm leaving" position. If you take the wider Men's Rights Movement one completely valid criticism is that while MRA's can sprout dozens of statistics (frequently true) about the ways in which life is hard for men... be it suicide rates, current earnings comparisons etc etc... they rarely if ever do anything about them. One doesn't have the be the biggest supporter of feminism (and as anyone who's followed my posts here can tell you I'm pretty dismissive of certain more recent strands) to be able to identify the succcess femenism has had... from getting the vote onwards. The Men's Rights Movement in roughly its modern form has been going since the 1970's... what campaigns or successes does it have to shout about? Increases in paternity leave in recent years (and I should note that's arguably also a feminist success; it allows a woman who's had a child to return to work while the father stays home without taking as serious a financial hit)? That's about it. I have a sneaking suspicion that the reason certain MRA's are happy to talk about how there are so few shelters for vulnerable men while being so reluctant to set one up is because that lack of shelters gives them a stick to beat feminists with. Compared to that, there is some merit in a position that doesn't pretend to be about changing the world, instead simply getting away from it.
On the personal level it's a horrible way to govern human interaction. And it borrows rather a lot (you'll see a theme here) from the more extreme wings of feminism that view all men as being "evil"... either inherently or because of the insidious effects of a patriarchy which they cannot escape... and/or use the "all men are capable of rape and thus the undercurrent of all interactions between a man and a woman is that he could rape her" and/or a whole bunch of other pretty damn extreme stuff. From what I've seen of MGTOW videos they're not just complaining about a system that favours women, they're seeing pretty much each and every woman as an evil Jezebel intent only on exploiting men. The extreme feminists will talk about how an undercurrent of rape applies to all interactions... the MGTOW crowd are pretty much saying the same thing but substituting rape for "alimony/child support payments" or false rape accusations. It's such a foolish position that it's hardly worth bothering to break it down.
As far as I can tell there is precisely one thing of worth to MGTOW and the whole "Red Pill" thing... and it's something PUA's have noted and worked on (hence their inclusion). You shouldn't value your own existence on how other people regard you... especially not how members of the other sex do. You're worth far more than that. Your self-worth should be based on far more than your relationship status. PUA's picked up on it (somewhat hypocritically considering that virtually the entire point of being a PUA is to define yourself by how you do with women) because there's something fairly attractive about having the confidence to know that it doesn't really matter if you get the girl or not and it's certainly not attractive to obsess over one (and I'm not talking the extremes of obsession complete with shrines, candles and badly written poetry) or to define yourself utterly by whether you "get" her or not. That's largely my issue with PUA as a culture/lifestyle... hell, even as a technique. I think it could do a lot of good if they became the person PUA's present them to be... confident, happy, sure of themselves. But PUA's don't. They pretend to be.
This touches on the whole "nice guy" thing... another point of similarity between MGTOW/Red Pillers and feminists. Both tend to have a lot of contempt for the "nice guy". The "nice guy" is the one who's attracted to a girl but is content only to be friends despite wanting more. He'll never press the issue though... that wouldn't be "nice". And as he pats her head and listens to her cry and complain after another failed relationship with a "bad boy" who mistreated her he sits there and thinks "Why do you keep going for bad boys? Why don't you go for me? I'm nice". But he never says it and six months later the cycle repeats again.
To the MGTOW/Red Pillers he's an example of how "pussy whipped" the world is, an example of a man who's given up their masculinity in a vain hope of pleasing a woman, an example of how pathetic modern men are. To the feminists the "nice guy" is an example of the entitlement culture and mindset they claim men have; when the "nice guy" says he's "nice" what he's really saying is "I was nice to you therefore I'm entitled to have sex with you." They see it as indicative of a worldview where women are sexual dispensing machines; you point kindness coins in, you get sex out.
I think there's actually a certain amount of strength to both views, although both still miss the mark widely. In my mind the "nice guy" isn't saying "I'm nice therefore I deserve sex"... he's saying "I'm nicer then these other guys you go with who always end up hurting you... doesn't it make sense to go for me?". And there's a certain rational strength to that position... which would be great if relationships and attraction were decided by rationality alone. They're not. But that's still not enough to label a "nice guy" pathetic or an example of what's gone wrong in the world. It is, at the end of the day, simply someone being nice.
So where does that leave us?
If you hear something about how bad the world is for men from a MGTOW type then double check the source but don't dismiss it out of hand; there are some things in this world that are pretty damn rubbish for men. But then don't just use it as a quick fact to pull out when debating with/shouting at feminists. Do something about it.
And don't define yourself purely by how you do with women be it in terms of one night stands or relationships. Everyone is far more than simply their relationship status. You may also find this also tends to work the other way; as long as you're still out and about the less you care about whether you "get the girl" or not, the more likely you are to get her. But again, you shouldn't be that bothered if you don't. It's deeply unhealthy to define yourself entirely by other people's opinion of you. That's not an excuse to go out and be a right arsehole while screaming "La La I don't care what you think of me"... it's just a reminder that happyness doesn't come from other people's thoughts of you.
Beyond that? Stay the hell away from those groups and that mindset. It's a nasty, crude, toxic position that tends to corrupt everything it touches. It's relationship with the extreme side of feminism is basically the horseshoe principle in action... they're not opposites, they're virtually identical.