The Idaho Values Alliance, which views itself as "Promoting and Defending Mainstream Values", is concerned about liabiity of Lake City High School for sanctioning a Gay-Straight Alliance. Here is the reasoning.
"GSAs claim to be about diversity but are really about promoting the normalization of homosexuality. Imagine a teenager struggling with his gender identity drifting into a GSA and being assured by a faculty member that being gay is perfectly o.k. Influenced by this authority figure, he experiments with homosexual behavior and contracts AIDS as a result. It is not hard to see the legal exposure the school would face in a situation like that."
That scenario playing out seems pretty remote, and even if it did, I don't see much proximate cause between sanctioning the GSA club and the kid getting AIDs. Also, there would be an intervening and superceding cause, i.e., the kid's choice to "experiment." Good grief. This kind of fearmongering just begs for the rightwingnut label.
I think the most likely lawsuit would be for discrimination if the school refused to charter a club that met all the legit requirements.