Civil unions.

And yet, none of these people will bother to examine their prejudice and what it says about them that the way they tried to minimize and dismiss concern for misandry is exactly the same mechanic used by homophobes. Almost assuredly, every feminist who has come out with this argument to deny there's such a thing as institutional misandry in this case or to minimize the concern believes in gay marriage and is opposed to civil unions as an alternative, and would consider the argument that it gives the same legal rights as marriage to be a cover for homophobia.

They will almost certainly not, if you point this out to them, consider where their misandry is sourced from, nor even engage in much self-reflection on whether there is more misandry in them and their worldview that they didn't notice until you showed them a mirror.

What does it say about feminism as a movement that it is the source of a meme used in rebuttal to our arguments that is functionally interchangeable with "Civil unions should be enough."?

More so, what does it say about their claims to care about men too that this fairly obvious contradiction in their thinking didn't occur to them?

These people think they care about men too because they never bother to check their beliefs, actions, and statements for misandry, and so they think they don't engage in it.

They don't check because they don't believe their worldview is sexist, and lack skepticism in that regard. Pointing this stuff out to them however usually doesn't prompt them to engage in self-review. I have to conclude that it's beyond mere dissonance, ideological flaw, or ignorance, there is an active lack of giving a fuck about men that perpetuates the behavior, self-sustaining in how it causes them to remain ignorant of their misandry and misandry around them and thus view men as a disproportionate evil in society, causing them to not care, as well as the ignorance justifying the ignorance in that it means they don't bother looking for misandry too because they don't think there's any/much of it, especially in their own doctrine.

It's an example of how many feminists impulse to dismiss or deny the extent and severity of misandry leads them to engage in it. None of them noticed this, because the worldview they use does not give them the tools to notice it.