Strategy to deal with hiring discrimination against gender nonconforming hairstyle?

edit for more context: I shaved my hair last month so it's unusually short. i've been asked if i'm a "buddhist monk/nun" by confused bigots, pushed out of bathrooms by binary women who thought i was a man, and stared at the streets when I go out with my natural hair.

I am an afab nb college student. I have very short hair for a “woman”. Way shorter than most men. I’ve been looking for private tutoring jobs and I’m worried about my hairstyle working against me. I live in a conservative area with basically no protections for queer people, so I know showing up with very short hair as a “woman” can seriously hurt my chances. a lot of employers ask for your binary gender and a headshot in my country, so if my appearance makes me appear masc, I will "attract" a lot of trouble.

I tried wearing a wig to interviews, but I don’t think it’s a sustainable solution because it’s distressing to go against my gender presentation and it undermines my ability to showcase my skills. So I’m considering alternatives:

  1. Show up with a beanie to conceal hair. This runs the risk of being seen as unprofessional, so tell tutoring companies/parents that I had a bad haircut and wanted to conceal it.
  2. Just show up in my natural hair and roll with the hate. (I’m not in physical danger but this can def cost me opportunities or ramp up hiring discrimination)
  3. Stop looking for jobs until my hair grows to an "acceptable" length. (I'm not desperate for jobs rn but it would be gross if I have do to this just because bigots can't look past my gender presentation)

What would you do if you were in my shoes?