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The problem, in my opinion, is that neither “idealism” nor the” scientific picture of the world ” are any formalized unambiguous philosophical systems. “Idealism” is a bunch of different philosophical trends and systems that are very different from each other. And the “scientific picture of the world” is, so to speak, a free translation by any person of some scientific theories and concepts into the language of philosophy. There are about the same number of such translations as there are people who have thought about this very “scientific picture of the world”. And they're all different, too.
If we reformulate the question as “is it possible in principle to avoid contradictions between some idealistic philosophical system and some scientific picture of the world?”, then the answer seems to be positive. A large number of scientists, in any case, perfectly combined their “scientific picture of the world” with a commitment to idealistic systems in philosophy.