Lanefan
Victoria Rules
Not necessarily.Yes. This strikes me as player conflict being channeled through their characters.
Could be - and IMO often is - the players are allowing their PCs to come into conflict with each other and leaving it all in-character; and having fun with it.
I've seen this done, and it always struck me as being just a bit too meta for my liking.If the players really wanted to get along, they would (as @iserith says) have fun narrating ways to "look the other way" during those awkward moments. I.e., some of the players agree to let the captive go, then they distract the paladin and kill the captive while he isn't looking. Or the paladin agrees to do the dirty deed and takes the captive off into the woods to off him, but of course lets him go. And everybody pretends to fall for it.
Again, false equivalence.Since they're not doing this, your problem is the desire of the group to play D&D as a group, not the alignments (or oaths) of their characters.
It's very possible and quite easy for a group of players to have their PCs fight like cats while getting along with each other just fine in reality at the table.