Physicists believe that when you look at massive objects over large distances, GR provides the right answer, while the QM is usually uncomputable.
Physicists believe that at small distances with small objects, QM gives the right answer while GR usually doesn't apply / gives nonsense.
They are both right, when you are looking at a specific circumstance, they only contradict when we are talking about Black Wholes and other objects that are small and massive or large (distance) with small (mass). Then physicists don't believe either because they both give nonsense.
No, they do not "contradict each other". They apply to different situations and there is some difficulty when you try to fit them together. Both have given excellent experimental results (GPS requires relativity to give accurate results and transistors are based on quantum theory). Presumably some theory that includes both quantum theory and relativity as special cases will be found- that's pretty much the way science works.
As others said they are used differently, Relativity is used when it comes to extremely massive objects such as stars. Quantum mechanics is used when describing small objects such as atoms and what happens within it. Now when you have to use both which is why there are some disagreements are which one to use when describing a Black hole.