There are important insights that I would like to convey here:
- All/Most interpretations of quantum mechanics predict exactly the same for all possible experiments.
- They do, however, strongly differ in the picture of the world they convey, and in the amount of conceptual clarity.
- One should choose an interpretation/formulation of quantum mechanics according to how useful, understandable and conceptually clear it is to us.
For point 1, the "interpretations" like many-worlds, Copenhagen/ operationalist quantum mechanics, de-Broglie-Bohm, ... have in common that they all give at the level of experiments a formalism with which you can calculate probabilities. These have been shown to be right over and over again in myriads of situations.
For point 2, you might want to read up about the measurement problem. This was a problem that came up in the early formulation of quantum mechanics by Bohr and Heisenberg (which is basically still in the textbooks), but it is not a problem in practice, because still the effective measurement formalism of Copenhagen quantum mechanics works great. But it is a problem in principle or for the picture of the world, it makes the theory less understandable, or less mathematically and conceptually precise. Most interpretations of quantum mechanics try to solve the measurement problem and do so better or worse. And by the way, one could really phrase the measurement problem briefly as: Copenhagen quantum mechanics only works on an operational level and does not tell you how nature really behaves.
For point 3, since there is no experiment which will tell us which interpretation to choose, we are mainly free to choose what we like best. This is not so new to physics and nothing which should be foisted off to the philosophers, because equations alone are not a physical theory, you need words to connect it to the world. The reasons for which we choose an interpretation can be manifold and this is the point in the on-going discussion about interpretations. There is no real consensus about the question "What is a good physical theory?". I would say, personal opinion, that understandable, mathematically and conceptually clear interpretations should be favored. They are easier to teach and, since they are equivalent, give you a good grasp of what happens in atoms and such.
And for the end: No, quantum "weirdness" (which is a bad word) cannot be avoided, since Bell's inequality and the experiments really reveal non-local causality, in fact, and you have to do quite some strange things to try and get around this.