In the particularly misogynist vernacular, to be cunty is to engage in nasty, vicious behaviour. Originally used to describe the moodiness attributed to women when their menstrual cycle rolls around, the gay (male) community co-opted cuntiness to describe bitter, vitriolic "bitchy" behaviour associated with a particular stereotype of gay men. Specifically, it denoted the state where good-natured teasing crosses the line into thinly veiled personal attacks.
KidKero came up with this expression to describe when someone (or, more typically, a group of someones) jumps right for the sardonic jugular almost immediately. People's feelings often get hurt when people are Too Cunty, Too Soon and the expression is used as a warning that perhaps the nastiness is getting out of hand. (see: cunt dial)