Socialism

It interests me in part because it seems to be an admission that even mild cultural nonconformity (non-approved hair colors, a piercing in the wrong place) upsets the right.

I don't think it's about cultural nonconformity, per se - there are plenty of people leaning conservative all the way to protofascist who will tell you they're nonconformist, and to whatever extent that might actually be true, a number of them take delight in the shock value that the expressed nonconformity provokes. This is all anecdotal, but I think when they talk about 'Purple hair, et al.' I think it has more to do with the objectification of women and how hierarchy and authoritarianism apply in conservative contexts.

Male conservatives, especially in digital spaces, view women almost exclusively in one of two camps: as wives and mothers, to service a man's needs before anything else, or as 'radical feminists' with any number of more derogatory terms appended. It's why they get so up in arms when a woman in the media expresses an opinion of any kind, on any topic, that doesn't conform strictly to that worldview, even when men on any part of the political spectrum express the exact same opinions. Any woman who dyes their hair purple, or gets a piercing, or a visible tattoo, wears suggestive clothing in public, or does anything to alter their appearance to 'anything outside of stepford wife territory,' is summarily filed into that latter camp, because the expression of individuality implies that a woman will see themselves as an equal individual, and when most conservatives see women as things to service male needs before their own, it upsets them when a woman exists alongside in the social hierarchy, rather than beneath.

Again, this is all anecdotal, but that's how I see conservative acquaintances talk about and treat the women in their lives.