WARNING FOR RANT - sorry, can't do spoilers:
I've never seen quite how gender/sexuality/style of expression of femininity or masculinity and degree of badassery are even supposed to be related, possibly because I have broad experience of women being badass in all kinds of ways. Men also. I get heartily sick of the kinds of feminist-separatists and Dianics who rant at me about betraying my gender (which is female) by daring to want, and to have children, when they think I could be so much more if I just narrowed my life down to fit their ideals. Grrrr! They annoy me nearly as much as the men who think I've betrayed my gender (that seems to be a favourite phrase with obsessed fanatics, for some reason) by daring to do 'men's jobs', or practise heavy-duty martial arts, or be alone in wild dangerous places.... also grrrrr!
And as for the expectation that because I am a tough and competent woman I will of course be rude, abrasive and discourteous, that's if I am not meek, quiet and submissive just because I am female...I don't have the words.
I just try not to worry about what people expect. If I want to work alone in the desert I'll do so, and wear the consequences. If I want to cook an exotic dinner for my husband, and wear perfume and take my hair down and write sonnets for him then I'll do that too. END OF RANT.
I don't know the character of Korra, but totally agree with you about Sigrun.