Can you have chemistry with someone incompatible?

Yes, unfortunately. Chemistry is neurological attraction that's sometimes random. You might have incredible chemistry with someone whose values don't align. After 6-12 months when the neurochemistry fades, incompatibility surfaces and the relationship crashes. Chemistry alone is not sustainable.

Can you build chemistry with someone compatible?

Sometimes, but rarely. Chemistry usually emerges early or not at all. If you're compatible but have zero attraction after 3-4 dates, additional dates probably won't change that. You can choose to commit to someone compatible without chemistry (companionship model), but it requires both partners' intention.

If I had to choose one, which matters more?

Compatibility. Chemistry fades; compatibility sustains. A deeply compatible couple with modest chemistry thrives for decades. A highly chemically connected incompatible couple burns bright and fast, then implodes. Choose the person you can actually build a life with.