Hopefully not. You're allowed to "advocate" anything you want except overthrow of the government. Merely advocating a dangerous activity is, and should be, protected speech, subject of course to the usual limits (yelling "fire" in a crowded theater, libel/slander, etc.).
Selling a product that enables a dangerous activity (e.g. cigarettes) can get you in trouble in some cases. So maybe these folks can go after the manufacturers of gay paraphernalia. But that's not going to be very effective, and it invites the Nanny State mentality.
Worse, the same argument could be used about fireworks, liquor, guns, and a host of other items that can result in death, which we would rather not have banned by the Nanny State.
I sense a slippery slope.
If it is possible to go after a diocese because a priest engaged in sexual misbehavior, why couldn’t one go after a diocese because that misbehavior led a victim to act out gay behavior up to their illness and eventual death?
For example, why couldn’t the employer of Rock Hudson (or his estate) be sued for negligently turning a blind eye to sexual predation leading to the infection of the preyed upon?
Why couldn’t my United Methodist denomination be sued for it’s bishop turning a negligent, blind eye to the sexual predation that accompanies gathering those with histories of same and turning them loose amidst potential prey?