"I actually don't think berating is a significant trope in feminist discussion"

There was certainly a fair amount of berating here in the UK a while back. There seemed to be a cottage industry in outing people who didn't want to be photographed wearing a 'this is what a feminist looks like' t-shirt (David Cameron was probably the most notable target). I also seem to recall there being a fair amount of discussion when 'are you a feminist' became a standard question for female celebrities and some answered in the negative. This may just be a UK thing though.

I don't think that it is entirely feminism's fault (after all, it is not as though 'feminism' has a PR dept who have dropped the ball). However, I do think that several prominant feminist commentators seem to be deliberately provocative (Jessica 'it wouldn't matter if I did hate men' Valenti springs to mind). It is an open question how much a movement bears responsibility for those who travel under its banner - can we dismiss the good work that some Feminists/MRA's do because we disagree with some of its proponents? I would suggest not, largely because I prefer to engage with specific arguments/claims rather than movements, but I think that majority of people are happy to dismiss the movement as a whole, and this makes PR a problem for feminism, even if it is not entirely of its own making.

I think you are wrong about why feminism is more of a target for this than 'RedPillers' (not a generalisation I am particularly happy with). Feminism now constitutes the majority of the public discussion about gender. This is a good thing for feminists, but it makes them a target precisely because they get column inches in mainstream publications (who often also offer avenues to respond). People writing about men's issues don't get the same exposure, therefore they have a much lower profile.

Another point to think about is that there is also a fair amount of disagreement within feminism which also gets in the way of getting stuff done. The recent TERF war springs to mind, for example.