Journalism in particular seems to be very radicalized. What you end up with is an outsized voice for an extreme minority opinion. I think a lot of the backlash against feminism is about the traction some of the more radical ideas have made.
Examples: #killallmen, male tears...
There are other extreme examples that have been codified in academia, but the media issues seem more cut and dry.
"Male tears" isn't a radical feminist thing, many non-radical feminists use it. Actually, it's quite the opposite, it's men who have always said feminist women (radical or not) are anti-men, so they decided to play along and made a joke about it.
While I think "male tears" isn't anti-men, I do think it could be against hegemonic masculinity, which is when men are told they have to be strong, non-emotional, etc; e.g. the past few days people have been talking about some research that implies that male gamers who harass women (i.e. they comply with hegemonic masculinty) are "losers", and some people have talked about it using #maletears. There's some anti-hegemonic masculinity Schadenfreude going on there. Some people think #maletears create a stigma around men who do cry, but it's also the opposite, it's joking about men who think they can't cry, they should be allowed to cry if they want to.
About the #killallmen, I think it didn't get traction where I live, in Brazil, I hadn't heard about it. I'm not sure what is it about, but I can see how some feminist women would argue that men do assault and kill women every day, systematically, so it could be sarcastic. Also, as something that would instantly backfire, it could be an attempt to destroy feminism from within, but you see, any feminist with a basic understanding of gender theory would immediately see thru that: men are not all equal, just as women are not all equal. So, let's say, if we're killing all men, what do we do to trans women? See, it doesn't work in a feminist framework.
"Male tears" definitely went beyond a joke as well. It's often used now to celebrate events that anger men.
If feminists (radical or otherwise) want people to take them seriously, they must treat people as they want to be treated.
"It's just a joke" most definitely doesn't work when it comes to men talking about women so it shouldn't be used in the opposite direction.
However, I do agree that in the context of a honest debate this really doesn't help, and I wouldn't use it there. But I know many people would, because in both sides so many people think debate is about winning, not conveying ideas.