Snapedom

Rowling said in her interviews post-DH that James was independently wealthy, which allowed James and Sirius not to worry about having jobs, so they could "work" for the Order full-time. Note that she does not include Lupin in James' largesse, which according to her extended to James' wife and Sirius, who just happened to be pure-blooded.

I had thought she said that James supported Lupin too, but maybe I misread it, or automatically assumed that Lupin was included when it wasn't explicitly stated. But either way, there must have some sort of falling out, or at least distancing between Lupin and the other Marauders after they left school, since Sirius so easily believed Lupin to be the traitor, and Lupin was apparently never considered for the position of secret-keeper though Sirius and Peter were.

I always wondered if it had something to do with the Shrieking Shack prank. Obviously Lupin didn't end his friendship with Sirius over it, but he must have been upset that he was used by his friend to carry out a stupid prank that would have gotten a human being killed or turned into a werewolf. Knowing how much he's suffered from his own lycanthropy, I'm sure that Lupin would have been devastated if he'd inflicted his curse on another person. And if James hadn't rescued Snape in time, that would probably have spelled Lupin's destruction as well. I don't know what the wizarding laws are regarding werewolves who attack people, but I would imagine a sentence in Azkaban at the least.

So yes, I think that Lupin would be pretty mad at Sirius, and since even years later in PoA, Sirius still isn't repentent about the prank, he might well be angry in return that Lupin is making a big deal about a mere prank--Snape didn't get hurt, after all. To him it might seem like Lupin is sticking up for Snivellus over his friends. They must have made up on the surface, but that might have driven a small wedge between Lupin and the others that gradually got wider with time. Maybe James and Sirius saw that they couldn't trust him to stand by them wholeheartedly, without reservation, and Lupin saw how little his "friends" (or at least Sirius) really valued him, if they'd risk his freedom and maybe his life to use him as a weapon against Snape in a stupid prank.

Or maybe it is just prejudice coming into play, and deep down, James and Sirius couldn't fully trust a werewolf and a half-blood (Lupin is both--a double strike against him).