I've always understood "tits or gtfo" to suggest that if you are mentioning you are a girl then do something related to it (show breasts) or else shut up about being a girl when its not relevant.
That's on the charitable side. It reads to me more like "a woman's acceptance in this community is predicated on her providing sexual favours". But your interpretation still reveals an issue: men are allowed to express themselves in small (and often large) ways that are "not relevant", so why this (pervasive) attitude when women do it?
I cant recall a single instance where the woman in question delivered and then wasn't met with immediate derision and misogny. It was a pretty explicit anti woman statement
