If the Amarrians ditched the entire concept of slavery, you could see an Amarr/Gallente relationship being built around culture and technology.
I'm not sure what the sticking point against it would be for the Amarrians, I'd considered lack of faith but it doesn't seem to stop them allying with the Caldari.
Also for the record, an Amarr/Gallente alliance would be horrifically scary in terms of Empire Navy strength, which is why fiction wise it'll never happen.
Leaving all game balance issues aside (which would, by the way, still be fairly balanced when measured in number of capsuleers, which I would say is the
real game balance concern), I believe the best approach to take in regard to Amarr/Gallente cooperation would be an economic one. Economy generally seems to affect international politics to an equal if not greater degree than ideology does (the real world is not short of examples of this), and if the current blocs disintegrate, it seems to me that there would be plenty of economic reasons for Gallente and Amarr to grow closer. They are both huge empires with huge populations and strong economies (however inefficiently it may be run in parts of the Amarrian Emppire) and consequently, huge potential markets. They are also both politically outward-looking, as opposed to the more insular Caldari and at least partly also Matari. In addition, while the Caldari and Minmatar societies have been suffering from a lot of political turmoil and instability in recent years, both the Federation and Empire seem to be quite internally stable, making them inherently more attractive to foreign investors, or so at least I imagine.
I'm not an economist, but that's how it looks like to me at least.
By the way, maybe we should have a thread split for the Amarrian-Gallente side of the discussion here?