"Please don't watch that movie yet."
Because the way that は sets the topic of discussion can have a useful contrastive effect. It's like you started with a whole shelf of movies, zoomed in on that one in particular and said please not to watch it yet. There's a bit of an implicit suggestion that maybe another one would be okay (without actually saying that).
With を maybe it's not just that particular movie, perhaps there's something else you want the listener to do first.
In particular, there's another sentence in this lesson where まだ is placed first. Why not in this one? Who knows...
I may be wrong, but I understood the は particle as a topic marker, indicating what the sentence is about, が as subject marker, showing what takes action, and を as object marker. So sometimes the topic could be the subject and the object, and could also be neither, like hehe: わたしは花が好きです So to answer your question, I think it could be both は and を. But I am no mother speaker so I'm not sure.
That's correct... For this line, は kind of makes this line work like, "That particular movie, don't watch it just yet"
Obviously, あのえいがはまだ見ないでください should be accepted. The word "that" is translated as 「その」 or 「あの」, depending on the situation. Reported on Oct. 30, 2017.