Yes, it does have an image problem. But then, this is how it works.
The civil rights era had an image problem. Women want to vote? Image problem. And on and on and on.
See, the image problem is not their own doing, but from outside of it.
Take a standardized term like toxic masculinity. Now, we all know what toxic masculinity means, but other people might not.
So because they don't know what it means, they're open to people co-opting the message and substituting their own. So instead of "Toxic masculinity is the societal expectation that men act a certain way and any deviation from this is unmanly, so it's unhealthy for both society and men both," it becomes "Toxic masculinity is the generalization against all men that because they're men, they are toxic, so they need to be stamped out."
Where before, the onus would be on people to teach others what they're talking about, now it's on them to defend why their term seems so accusatory and 'anti-men.' The more resources you put into fighting that latter battle is the fewer resources you have to fight the former.
Or, to put it plain, in an ideal world, we shouldn't have to literally police our tone and explain in public what terms mean when we use them in any particular subject. But because people are fucking morons, and the ones that aren't fucking morons have vested interest in shutting you down, your image starts to suffer.
Put it plainer, we aren't in an ideal world and this change has to happen mostly uniformly or else it will be met with massive backlash and may never actually achieve anything.
So when you talk a bout toxic masculinity, assuage the fucking idiots. "Toxic masculinity, or the idea that if you're a man, you aren't allowed to cry ever" or "toxic masculinity, the idea that if you're a man you aren't as good at caring for your child as a woman" or "toxic masculinity, the idea that if you're a man, you're going to bust your ass working until you die because that's all you're good for," or what-have-you.
It has an image problem because people with vested interest in the status quo beat the average internet dweller to the messaging punch. Now we have to fight the falsities and still find time to offer alternatives.
My advice is that the image problem that suffragettes had didn't stop women from getting the right to vote...and let's be honest, here, but the anti-social justice crowd are basically just reusing the same bullshit propaganda from that time, anyway. Best not to worry about it so much.