St. Brandon writes about problems in philosophy, but a lot of what he says seems applicable to physics as well. In my field of quantum gravity, there's no experimental evidence so a lot of the back-and-forth has to do with identifying conceptual problems with different ideas. It's not always easy to know which problems are fatal to a theory, and which should be viewed as an impetus to more research.
On a side note, we love to talk about the beliefs of scientific researchers (do you believe in string theory or loop quantum gravity or something else?) but in fact beliefs don't always directly affect how one does research. The most important thing is what questions one thinks are worthy of further investigation. Two researchers may be developing the exact same argument A, even though one person is trying to work out the consequences of idea X, while the other is trying to refute X by a reductio argument. However, it is important to have enough flexibility of mind to realize when you have accidentally constructed an argument for the other side.
On the other hand, beliefs do matter indirectly for structuring research, because they help determine which problems you think are worthy of study, and what factors you take into consideration. Also, they obviously help determine what conclusions you draw when you're done. Beliefs about how one should structure an inquiry may be more important than beliefs about what the final conclusion should be.