Would going off birth control make my fungal folliculitis better, worse or have no effect whatsoever?

Varies: The effect of oral contraceptives on various skin issues varies from person to person. Worth a try to go off the pills and see what happens, meanwhile use alternatives to the pills. I assume you have had anti fungal treatments already.

Fungal infection: It may make it worse, which is why it is always good practice to treat a fungal infection and eradicate it. You didn't say where the infection has taken hold, but I would consult your dermatologist or Gyn specialist if it is in the pelvic area, and get it treated.