CAUTION: I'm not a native English speaker.

I've just come across this post. IMHO all versions are illogical if not incorrect. Whether the subject is missing in the main clause ("doesn't mean...") or it is a pronoun that is supposed to refer to the subordinate clause, the subordinate clause must respond to the question "what doesn't mean...?". However, a "just because..." clause responds to a question "why?".

Better variations could be
"The fact that I was mean to you doesn’t mean you should be mean to me."
("The fact that..." responds to a "what?" question.) or
"Just because I was mean to you you shouldn't necessarily be mean to me."
(The main clause is complete and the subordinate clause may have the function of a causal adjunct, responding to the question "why?".)

The fact that there is no uncomplicated solution stems from the fact that while both the subject and the object respond to a "what?" question, only a subordinate clause that substitutes the object can be introduced with "that", one that substitutes the subject cannot:
"I think that I was mean to you." (Correct, the subordinate clause represents the object of "I think".)
"That I was mean to you doesn't mean you should be mean to me."* (Incorrect, the subordinate clause represents the subject. I don't know any reason why it is wrong other than it sounds wrong. Note that in my native language, Hungarian, its equivalent is perfectly correct.)
Since this is incorrect, it needs to be worked around with the ill-sounding "the fact that" or the illogical "just because".