If you go to the FR Wikipedia entry, the Neogi proverb at the top says it all: The enemy of my enemy is my enemy.
They're xenophobic - they hate anything not Neogi. That site also has some references to the ways Neogi interact with Djinn and Gith (hint: They're prey). Neogi
They see everything out there as either enemies or slaves.
In my homebrew setting they are hated by all other races, but evil intelligent beings are willing to negotiate with them (carefully).