Complex sentence: The Studio became an alternative to the state system of cinema and theatrical education, but it did not oppose itself to the "official art", but, on the contrary, aspired to removal of oppositional difference between the tradition and avant-guard.
Split into simpler sentences: The Studio became an alternative to the state system of cinema and theatrical education. It did not oppose itself to "official art", but, on the contrary, aspired to the removal of oppositional difference between the traditional and the avant-guard.