Learn Hardcore Russian: Не будь съёмочной группы, короткометражку бы не закончили. - Were it not for the film crew, the short film would not have been finished.

Breakdown of Не будь съёмочной группы, короткометражку бы не закончили.

What does Не будь... mean here?

In this sentence, Не будь + noun means if it weren’t for... / had it not been for...

So:

Не будь съёмочной группы = If it weren’t for the film crew
Whole sentence: If it weren’t for the film crew, they wouldn’t have finished the short film.

This is a compact, somewhat literary way of expressing a condition.

Is не будь literally an imperative, like don’t be?

Formally, будь is the imperative form of быть (to be), so it looks like don’t be.

But in this sentence, that is not how it functions.
Не будь + Genitive is a fixed conditional expression meaning:

So here you should understand it as a set construction, not as a real command.

Compare:

Не будь грубым. = Don’t be rude. ← real imperative
Не будь съёмочной группы, ... = If it weren’t for the film crew, ... ← fixed conditional pattern

Why is съёмочной группы in the genitive case?