That’s a slightly different question I think, because technically 映画見る is ungrammatical, but it is natural to hear and use in casual speech. 勉強する on the other hand is grammatical and normal in any register.
The main difference with 勉強する and 勉強をする is whether the preceding grammar demands one or the other.
See these for instance
日本語を勉強する 〇
日本語の勉強をする 〇
日本語の勉強する ✕
日本語を勉強をする ✕
And then, applying the concept from that video, 日本語勉強する can be heard in natural speech, but is technically ungrammatical.