If people thought that flood stories from different cultures may have been the same stories, then they would have been deeply mistaken.

Assuming some rephrasing is permitted (rather than simply changing word order), the following sentence works:

If people thought flood stories from different cultures possible variations of the same story, they had a deeply mistaken perspective.

Please give me the sentences before and after this one. I'm not sure what you are trying to convey. Are you saying "if" to indicate this never happened (and being wrong would have been the outcome had it happened); or that it possibly could have happened, but you aren't sure?

I may be wrong, but I believe that the conditional (if... then...) automatically forces you to use "to be" one way or another. You'd have to change the basic meaning of the sentence to get rid of "to be" (and I get the impression you don't want that).


(Edit)
Thinking it through some more, here's a suggestion that I don't think changes the meaning too much:

It's possible that people erroneously think that flood stories from different cultures may have the same origin, if that's what they believe.


(Edit #2)
I like benz's suggestion below, but I'd change it slightly to get rid of the tense inconsistencies:

If people thought flood stories from different cultures may have come from possible variations of the same story, they would have a deeply mistaken perspective.

Good luck,
- Gonzalo

If people think that flood stories from different cultures are the same, they are deeply mistaken.

If people thought that flood stories from different cultures were the same, they would be deeply mistaken.

Just a try :)