What you call the Buddha’s teachings is ultimately no more than connecting to reality so that you stop suffering from things that are not real, the things you think about.
Modern science deals, not so much with reality, but rather with the building and testing of models.
Nondual Buddhist and other wisdom traditions emphasize the transparency or lack of referent of all models. Knowing what is real, and more importantly, what is unreal – everything you and I think – so that you cease suffering from non-existent problems, those apparent problems that stem, not from what is happening, but from the way you think and create ideas.
So you could say these are neither compatible nor incompatible. In reality, resting in the unconditioned mind we find neither compatibility nor incompatibility.
Science aims to provide good models of what you observe.
Buddhism, on the other hand, aims to stop unnecessary suffering.