I alternate between a vegetarian and pescatarian diet (the latter purely for health reasons), and my partner avoids dairy and red meat. The meals we share, as a result, are vegan, though neither of us follow a vegan diet exclusively. We often cook meals just for ourselves and then eat them together.
I think the key here is that we both respect the other’s eating choices, rather than belittling them (something I’ve experienced previously).
As with so much in relationships, the most important factor in compatibility really is simple respect.