Aren't they opposite of each other?

They are sort of opposites, but their end affect is the same, much like the artificial divide between capitalism and communism. Marxism seeks to make everyone entirely equal, Anarcho-capitalism de facto makes everyone equal by eliminating the state. Equality is impossible, though, so in both cases, a heirarchy forms.

Like most humans you seem to be having trouble separating the concept of morality with legislation. Minimal legislation does not mean minimal morality and no values, that is a big conclusion to jump to. Morality will always continue to exist on a personal basis, the only difference being that everyone doesn't have to bend to fit the specific morality of the rulers. Most people will still almost certainly play bandwagon and follow the leader, I just don't see why we have to oppress dissidents other than it's our wild tribal nature and we get a high from it.

Legislating morality makes it much easier to enforce. Vigilantism is flawed due to human perception and mob mentality, and can't effectively regulate something long term. Lynch mobs are short, spring-up events that undoubtedly also would result in lots of separate issues.

The state is an unfeeling, organized mob. It's like an octopus, the individual arms are connected by a greater whole, and those motile arms can do what they please within the extents the body allows them.

The state is in the unique position of having lots of power and bureaucracy on its side, which unorganized mobs simply cannot achieve properly. This bureaucracy allows fairness and a precise system of dealing with degeneracy and the ability to snuff out issues before they arise (i.e. shutting down borders or launching military expeditions to snuff out drugs before they become a problem) and codeified laws allow a fair but effective method of determining who/what is an issue and how to deal with issues in a way that is most effective.

Because the right wing ones usually want to appear to have strict morals, so they're not going to admit to it to save their life. But they are caught in it just as often.

That's a good point, but Right Wing groups also police themselves a lot more. Look at the Night of the Long Knives: It may have mostly been a power move and political chess turn at heart, but eliminated degenerates like Ernst Röhm (who was a sodomite and pedophile) as well.

In general, all political movements could benefit from a sort of commisariate to weed out degeneracy and corruption. To balance such an organization would be difficult, as would havign them police themselves, but it's always an ideal to work towards.