A lot of these are social policy rather than norms, but:
Social norms in general, and the idea that they’re compulsory. I’d like to see the back of that. There are many ways to live life and society shouldn’t facilitate the idea that the married hetero nuclear family is the only proper superior way. I feel similarly about other more trivial norms like needless table etiquette (balancing peas on the back of a fork anyone?)
The traditional concepts of masculinity and femininity, and by extension, heterosexuality always being assumed as the default. I don’t see that actually benefiting anyone. It should be absolutely normal for men to be primary carers or equal parents, have flexible working, do chores and pick up the mental load (but I do unfortunately think women facilitate useless men too, unintentionally, by buying into the traditional feminine persona and therefore feeling compelled to just do this stuff rather than drawing a strong boundary and demanding true equality). Likewise it should be normal for women to have shaved heads and drive lorries and never want children if they so please. I don’t think the traditional set-up is really a free choice in our current society when other options are so discouraged.
marriage. Just abolish it completely and all the misogynist guff that comes with it (changing names, father giving you away etc). don’t even get me started on the wedding industry.
Consumerism and capitalism. It’s not a binary choice between that or dictator-led communism. The norms that arise from this like the fetishisation of homeownership and the “keeping up with the Jones’s” culture - burn it all. Universal free childcare, house price caps, nationalised services etc.
British prudishness. Nudity is not inherently sexual or shameful or taboo. We’ve all got the same bits, get over it.
the idea that men and women can’t be friends without something nefarious going on.
the idea that you shouldn’t simply say “no thank you, that’s kind of you to invite me but it’s not my bag” to an invitation you don’t want, and have to make up a convoluted excuse instead
The notion that you MUST bring a gift or money to a wedding. Perfectly fine to turn up empty handed.
There’s probably more as I find a lot of things annoying!