Would the legendary creature rule affect the gods?
ex. I have 2x {Thassa, God of the Sea} out but neither are creatures
Yes because the "legendary" rule doesn't a only apply to creatures. It applies to all permanents.
Edited with the ruling:
704.5k (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=704.5k): If a player controls two or more legendary permanents with the same name, that player chooses one of them, and the rest are put into their owners' graveyards. This is called the "legend rule."
You cannot control both at the same time, the only thing it gains and loses is the "creature" part of it, the legendary part is always there.