It's such a touchy subject because feminism definitely came about as a response to toxic masculine behaviors that have been around and are still with us. And while capitalism/toxic masculinity is to blame for most of men's mental health problems, at the same time, I think there's still been something of an overreach with feminism and there's actually some aspects of Western life where women are at a definite advantage, namely in the Court systems when dealing with divorce and custody issues. Men and women in these spaces are not treated equally and it's just accepted as "That's how it is," because we're ok with going off of outdated ideas in that space.
Having said all that, I still don't think it's fair to blame feminism for men's mental health issues, it's more just a societal thing that men in general are really considered expendable and left to fend for themselves on most of their problems. While I think it's gotten better over the years and it's more acceptable to at least talk about some things, there's still just a general apathetic attitude towards men's mental health issues. Men/Fathers will often be relied on by everybody else in the family for all sorts of things, but who does Dad have to turn to when he has problems? Mothers are often placed on a pedestal, and that's great for them, fathers though are just kind of... "Oh, it's you."