When you don’t own a horse, it’s not quite so personal an insult. (YMMV in the UK, if they still say knickers) It’s like insulting someone’s horse. Is ‘knickers in a twist’ less dismissive? I think so, at least in North America, because we don’t wear knickers.
I don’t see male opinions being denigrated with ‘oh, knock the crust off your dick’. ‘Panties in a bunch’ and its cruder cousin ‘knock the sand out of your vag’ infer that a woman’s opinion is borne from having a genital irritation as opposed to, you know, observation, knowledge or experience. The British expression 'kickers in a twist' goes back in print at least to 1969 and refers to womens (or girls) underwear becoming twisted and therefore uncomfortable and objectionable. There’s a long history of blowing off women’s opinions with accusations of being irrational, hysterical, strident or other terms that allowed us to be treated as stupid and safely ignored. You may not intend to imply that (consciously, at least) but that is the message you are sending. When you drag a sexually specific term into an argument, then (besdes the ad hominem issue) you are implying that the person’s gender is part of her wrong (according to you) point of view plus, the metaphor suggests it’s emotion and discomfort, not logic, that is guiding her point of view and using female-specific garmentology, that it is because she is female.