The specific gags (satanism, bisexuality) are generally more “left” but the polygamy* and downright stupidity are pretty par for the course. Every single time he says a variant of “I will fight for your freedom” it is followed up with “And here is a deviant thing I do”

Which has always kind of been the reality. The “Conservative Freedom Fighter” is basically just your bog standard Libertarian and has always been demonstrated to not actually care about freedom so much as the freedom to do whatever they want. The actual “I will fight for your right to be a piece of shit” has always been a byproduct of separation of church and state, etc. So… Liberals (and so is some of the stupidity…).

This was VERY early 00s and we had just had a decade of libertarian propaganda (seriously, look up MTV. It is frigging insane. And South Park was largely at its peak), so there was less outright calling people on their bullshit and identifying where “freedom” stops for them. But that is how conservatives have always justified their bullshit and, aside from changing what counts as being “deviant”, the gag works just as well today because it is still the same gag.

*: There is an argument for polygamy being related to ethical nonmonogamy, polyamory, etc. But at the time it would have very much been a Mormon gag. And… there are still arguments that the ENM movement has largely been compromised by misogynists and right wing lunatics. True ENM is still very much about social justice and accepting people for who they are, but it has also kind of become a bit of a red flag in social interactions.