In many hours of MP play, I have seen no sign of anything that is affected by the relative diplomacy scores between two players.  I can try bringing up my scores during my next session, but I don't expect my opponent to know, really.    

Using an unlikeable race can be a good strategy in MP unless you are in a crowded map with lots of AI acting as a buffer between the two of you.  In my case, it is obvious I am unlikeable because they very often declare war on me first, multiple factions at a time.  Therefore, it does have an indirect effect but nothing that affects human to human diplomacy. At least, it doesn't affect what you can trade or what values you place on those trades. My diplomacy attitudes are unpredictable enough as it is, I don't need some arbitrary game setting reaching out and making me act erratically. I can do that all by myself.

I've read all the replies so far. it seems diplomacy really does only AI players and not other human players. That's unfortunate. It is, however, a bit of a relief to see that it can have an indirect effect in multiplayer when there are also AI players as erischild mentioned. I'm not sure how often AI players exist in multiplayer games because I have admittedly not done any multiplayer yet

Hopefully, Stardock does something about this in the Crusade expansion. Maybe they could do something like make the player's civilization get morale boosts or penalties based on how they treat other civilizations versus how the people of the former civilization think about the latter civilizations. After all, the people of a civilization don't always agree with their leader(s).