First, saying "stone age beliefs" is hardly hate speech.  It is a bit inaccurate though, so perhaps "medieval beliefs" is a more apropos.

Second, if a parent is completely loving and supporting they should have no fear.  If their kid is afraid of "coming out" to them, there is a reason....and it most likely originated from something the parents have said or done that leads them to believe that their parents would not be supportive.  Instead of worrying about whether their kid might be part of such a group, perhaps they should worry more about making sure their kids know that they will support them unconditionally and that they need not fear bringing ANYTHING to their attention.