editorials - especially on the rightI know you don't intend to do so, but assuming that someone's conclusions about an issue must have come from talking points, and were not arrived at independently, dehumanizes them and makes it difficult to convince them of anything.
It discounts the lived experiences of people who have seen their friends and coworkers radicalized against them, of either gender. "This happened to me" cannot successfully be countered by "stop parroting X/Y/W-wing editorials." (general pattern I've seen even among family, not necessarily your phrasing)
The terminology used also doesn't help make the case for feminism among anyone not already convinced. Terms like "the patriarchy" can be seen as implying that it's okay to talk about men as a whole group who can be vilified, but it's not okay to talk about women in any negative way at all. Or "ally" could be seen as implying that the only identity someone not of group Z can have that matters is as an accessory to their cause.
The most disappointing and insulting thing a friend has ever said to me might be (paraphrasing) "I thought you wanted to be an ally." No, I wanted to be your friend, not a footsoldier who dutifully agrees with you 100% of the time no matter what my independent experiences have been.
I don't think it's helpful to think of "feminism" as a singular movement,
Sadly, even some of those who advocate for feminism (whichever branches might be considered "the good kind" for purposes of this discussion) seem to deliberately lump feminist movements together, so one can be forgiven for seeing terms like "the patriarchy" used by different groups and not knowing which group's beliefs to ascribe to the term. I don't think this can be blamed on a particular flavor of media, except maybe social media.