Synonyms for Compatible (same or very similar meaning)
WordNet sense 1 ((of a couple) existing together harmoniously):
well-matched
WordNet sense 2 (going well together; possessing harmonizing qualities):
matched
WordNet sense 3 (having similar disposition and tastes):
sympathetic
WordNet sense 4 (suitable to your needs or similar to your nature):
congenial
WordNet sense 5 ((chemistry, physics) capable of being mixed):
miscible, mixable
WordNet sense 6 (existing together in harmony):
harmonious
WordNet sense 7 (suitable or appropriate together):
congruous
From the ODE community, based on WordNet
add/edit