Which way is correct? 1. The class's actions are unacceptable 2. The class' actions are unacceptable?

The second one is correct if you have one class and it has some actions that are unacceptable.

If you have two classes, you should write: The classes' actions...

BUT, I'd just rewrite it to say: The actions of this class are....

M F, if only one class is involved is is 'The class's action'; if more than one class is involved, it would be 'The classes' actions'.

The general rule regarding words ending with 's' (in the singular) is that you should use apostrophe 's' for modern names and words, but 's' apostrophe for classical names and words. So, for example, you would write

Julius' sword; Cassius' armour; Brutus' plot to kill Caesar BUT

Denis's shoes; Francis's house; Ross's book

It depends on how many classes you are talking about. If it is one class, the first one would be correct. if it were two or more classes, it would be the second one.

Actually, it depends upon where you live. If you live in the US, the first one is correct. If you live in the UK or the Commonwealth, the second one is correct.

So, both are correct. Use either. You won't be wrong.