I've long said that the terminology of "left/liberal/democrat versus right/conservative/republican" in American politics bugs me because each side of that alleged spectrum isn't a single idea, but a random amalgamation of unrelated ideas artificially lumped together.
I was right, but I think it might be helpful to pinpoint exactly what ideas are being conflated on the left-right axis. There seem to be five different conflicts, and they're found together so often just because of local groupthink and self-perpetuating parenting.
Axis 1: Equality versus peace.¶
This goes outside of government. It's not a hard rule, but leftists often favor artificial equality that disregards individuals' differing merit, while rightists are more disposed to judge individuals on their actions even if their actions are unequal.
Axis 2: Gender roles.¶
Rightists tend to believe that gender has some kind of divinely ordained meaning (even if they wouldn't put it that way) and that it determines to a significant extent what role a person should play in society and in their relationships.
Leftists rejects gender roles.
Axis 3: The perversion of sex.¶
Rightists tend to believe that any type of sexual activity not between an adult man and an adult woman and formally recognized by an authority (usually a church, or the government for an atheist rightist), or outside of a lifelong, exclusive commitment to a special relationship, is inherently and extremely depraved.
Most leftists, on the other hand, believe sex has no special value and is a way of deriving pleasure like any other. They'll often defend pornography, prostitution and such even from peaceful disapproval.
However, leftists still usually abhor pedophilia, even if it's totally consensual on both ends.
Axis 4: The invention of gender identity.¶
Opposite to their rhetoric about gender being unimportant, leftists see gender as a psychological "identity" chosen by the individual and you're a hateful bigot if you ever suggest that changing your "gender identity" is a less-than-admirable thing to do.
Rightists do not invent a fake concept of gender as separate from sex.
Axis 5: Partisan counter-bigotry.¶
Leftists insist that there's (in America) serious widespread bigotry against women, non-whites, non-hereosexuals, Muslims, and the disabled. Rightists tend to perceive American society as mostly non-bigoted.
Whatever the fact of the situation, many leftists are so attached to fighting perceived bigotry against those groups that they've developed some degree of counter-bigotry against the "dominant class" of white, straight, cisgender, upper-class males. And I'm not just talking about the double standard on physical assault that you see quite often even outside of movies (conservatives seem to be just as guilty of excusing that); some liberals are way worse (be prepared for explicit content if you follow that link).
Libertarians, far less often discussed, tend to have all of these axes right except axis 3 (where you can often hear them glorify pornography and even prostitution). I think this is because "libertarianism" is the only one of these labels that actually maps to a single idea: self-ownership (or in Protagonist terms, the valuation of consent as close to the only moral value). Libertarians are the most consistent, although to really be consistent in that idea you have to be an anarchist.