Comment by DiogenesKynikos

Quantum mechanics and General Relativity[0] are not fundamentally incompatible. It's just that the most straightforward approach to incorporating gravity into the Standard Model fails. In fact, we know that it is possible to construct quantum theories of gravity that reduce to General Relativity in the classical limit. String Theory is one such theory. We just don't know if it's the correct theory.

0. Special Relativity is already baked into the Standard Model, which is a quantum theory. It's General Relativity that causes problems.