I can't speak for every case where they should be sued into the ground, but wouldn't the person they're defaming be the one that has to bring the charges? The shooter isn't in much of a position to do so (unless the family can?).
I'd love to see some LGBT+ organizations bring charges since they're drumming up this rhetoric to stir up hatred toward that community, but I honestly don't know if they would have legal standing to do so.