Are you disagreeing or are you asking for sources on the subject?
The "popular" MRA (mens rights activist) organizations use this very clearly barbaric practice as a pipeline. The people advocating against it in MRA are not pointing to the vast majority of feminist organizations that are against it. They are using it as a "wedge" issue and pretending that it is feminist themselves that are ignoring or even causing it.
Its similar to how many MRA people will say "woman need to be a part of the draft too". Instead of siding with the leftist and feminist organizations that want to abolish the draft altogether.
These organizations are rarely looking to improve mens rights; but pointing to issues like these as means to maintain patriarchal constructs. It is a means to keep men focused on the issues that impact them; but keep them from organizing or finding solidarity with the leftist movements that address others issues as well.
The vast majority of men are hurt in some way by the patriarchal structures of our society. But, instead of rightfully realizing that these issues are a RESULT of patriarchy they instead focus on them as a reason for why patriarchy doesn't exist.
It's because they think (maybe you included?) that patriarchy is just a measure of the "fairness" or "equality" between men and women. When it is not this at all. It is a interwoven with class structures, racial structures, and gender roles. "Intersectionality" if you will. The liberation from these structures would free men as well. But, the majority of them do not want to acknowledge the areas in their lives that they benefit from from patriarchy. They just want to maintain the status quo and remove or "make equal" a couple things that they don't like: parental rights, genital mutilation, the draft.
Which is why MRA groups are not taken seriously by the left. Not because the issues they have are not real. But because they do not acknowledge the issues of others within the same system that causes the MRA issues. It's not that leftist and feminist don't care about these issues. It's that these issues have been captured by the right to cause division.
It's very easy to look in your own bowl and see what is missing. But it's much more difficult to look in your neighbors bowl and see what you have that they do not. MRA movements are largely focused on what is missing from their bowl and in the extreme are looking to take from others bowls to fill theirs. "Women should be in the draft" is the obvious one. They want MORE class oppression as a means of "increasing equality". When we on the left realize that the draft is a result of class structures and not just patriarchy.
And, again, these groups don't actually want women in the draft. They just use this issue to capture men that feel powerless. Why do you think the right wing fascist want only men in the military? The military represents power. The draft for men and boys IS a structure of patriarchy that pulls in men with the promise of "power of women" and exploits the working class as labor for the war machine.