Why would characters adventure together?

[qube]

I understand diversity, but if player A is playing the stereotypical LG human paladin, and player B is playing a bloodthirsty CN lizardfolk barbarian, why would these 2 characters ever decide to adventure together?

That's something your characters should decide.

Especially if you give "free reign" to play evil characters - they should create (part of) their back story together. Otherwise, I predice in 2-3 sessions they will start to murder eachother, becasue "that's what their character would do".

My bias aside, how would the NPCs/townsfolk, in a mostly human setting, react when they see said lizardfolk (or any other monstrous race)?

that depends on the setting, the people, the monster, and how immersive your DM is.

I have DMs where I know this won't be a problem at all.
I have DMs I know I don't have to try and show my face or get attacked by city guards.

How would social encounters play out? Would the paladin (or any other character) shun the lizardfolk (and therefore the player) because of the social difficulties that character has forced upon the rest of the party?

again, up to the groupo.

Should all the characters be forced to adventure together just because they are played by players at the same table?

No. That simply doesn't work, because players are human. It's supposed to be a game, and everyone should be having fun. If there's someone who's definition of having fun includes "screw the rest, I'm having fun in spite of everyone else", then that person has to have a chat with.

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If you're the lizardfolk player in this scenerio ... talk to the (out game) group becasue they go no reason to accept homocidal monster in the (in game) party

If you're the paladin player of this scenario ... talk to the (out game) group, because I got a feeling either your paladin will fall or you'll end up killing that lizardfolk. Find a reason to work together, or solve this issue by talking person to person.