I don't think that having a mixed species crew in and of itself needs to be a stand-out thing. We risk destroying our own world because we're fighting each other, but honestly if we still had Earth and we encountered a potentially hostile alien race? Well, nothing makes humans put aside their arguments and band together like an outside threat.

Actually, another idea-

Could be that Humans were just starting to set up colonies on other planets in our solar system when the Yuan-ti war started, and unknown to us our system was more or less in the crossfire. An alien warship stopped in our system to do repairs, and they reacted with hostility when they found that there was curious life in this system. What they didn't expect was for the hugely outgunned Humans to end up working together to fight them, eventually taking the warship for themselves and killing the creatures that had "invaded" the Sol system. The technology from the alien craft catapulted human technology forward by a few generations in some fields (especially in regards to ftl travel) and so Humans set out into space, intent on heading off this threat before it could attack again.

They were a bit surprised when they found out that they had taken out a warship from the losing side of an intergalactic war, and in doing so earned the respect and allegiance of the side that wound up winning, along with the enmity of all those on the side that lost.

This sets up the humans as the fairly scrappy new kids on the block, that the other races don't really have a clear idea of yet. After all, they were just poking around with interplanetary flight until they took out a HIGHLY ADVANCED WARSHIP using highly outclassed ballistic weapons and chemical rockets, and that launched them forward into intergalactic flight and energy weapons.