I was actually a fan of Anton LaVey and his “Church of Satan” back in the day. At best, those only PARTLY line up with what they were talking about. Like #3, the “survival of the fittest” thing…yeah, LaVey was kind of a believer of that, but he certainly didn’t advocate for a “lack of compassion,” at least not for those you actually care about personally. If I am recalling it correctly, one of the rituals outlined in his book “The Satanic Rituals” was literally a “COMPASSION ritual.”
Oh, and also, I find that when anyone accuses some other people of believing in “moral relativism,” what they really seem to be saying is “they don’t believe the same things that I do.” I think most everyone practices some form of moral relativism to SOME degree. “Thou shalt not kill” is one of the famous 10 commandments in the Bible, and of course one most people of other religions or of none would generally agree on, but also even a lot of Christians would say some killing is justified, like in self-defense or the death penalty for violent criminals/murderers, etc.