I tend to argue that most of the issues of our time come down to supremacism being the biggest threat. Misogyny and patriarchy are features of male-supremacy, a movement that has dominated for centuries.

Hating men is a thing and honestly those women tend to have reasonable reasons for it but there is no real female-supremacy movement. Their participation is only in breaking male-supremacy.

Almost every issue of our time can be broken down into factions of supremacists vs those who oppose supremacism. Gender is a male-supremacist issue, lgbt is a hetero-supremacist cis-supremacist issue that ties into the male-supremacist issue.

To understand whether or not something should be entertained by the left you should simply analyse it under this framework. The term misandry is used exclusively by the male-supremacists has a means of painting part of their opposition as "too extreme". Which is rich when they are male-supremacists and these women they point the misandry finger at are just fighting against that.

Maybe you can find a person or two who will say "I believe in female-supremacy" but there is NO movement for it, no organisation for it, and it will never ever happen.

Now, look at our current global positions on imperialism. We understand that the biggest issue is imperialism which is again a supremacist issue (west/white). Under this we understand that there are two positions, the pro-supremacist side and the opposition to supremacy. We come down on the side of the opposition, 100% of the time, even when they're imperfect, and we call it "critical support". I argue that these are the same things, and that the position anyone should take with regards to it should be the same. The people the supremacists call misandrists are the assad and iran of gender-supremacy issues and our position on them should be identical to our position on imperialism. The supremacists scream about them because they recognise a potential group to peel away from their opposition, which disunites their opponent, which weakens their opponent.

Misandry is generally just a word used to browbeat the feminist movement into being less radical and thus less effective as an opposition to male-supremacy. But if anyone does exist that is functionally as bad as the male-supremacists claim that misandrists are then the correct position is still critical-support in the framework of anti-patriarchy, matching the framework of critical support for problematic sections of anti-imperialism used as movement-splitting.

Anyway most people I see getting called misandrists don't actually hate men, they hate male-supremacy and this is painted by the supremacists as hating men. If your position is opposition to misandry then this immediately backfoots you by forcing you to argue about how someone is not a misandrist. If your position is critical-support to them anyway then this just becomes "I don't care because the primary issue is defeating male-supremacy" and is barely a speedbump.

EDIT: Also if you bring critical-support into other movements you normalise it and unify strategy. It becomes very easy for people from one movement against supremacy to join other movements against supremacy because it all maps 1 to 1. We should be doing the same thing, in every movement. You want feminists to come over to anti-imperialism? Well if they're using all the same strategies and analysis we use in anti-imperialism then when you explain anti-imperialism to them it all becomes "aha that makes sense!" much more quickly.