Did the nuclear tests really affect Godzilla?

no he wasn't affected by it, but its not disapointing the original godzilla was not mutated only the heisei godzilla

I don't think he was mutated or was affected. Apparently the MUTOs have an EMP pulse to "disable" Godzilla's atomic breath. So that means he would've had it in the prehistoric times.

As far as the original, they said in the movie that Godzilla was from the Jurassic Period 2 million years ago (they said this constantly, even though the Jurrasic age was closer to 400-500 million years ago.) The original offered no explanation behind his atomic breath (that I remember), so I've always assumed that was a product of the bombs as well.

Really @CATZILLA? As far as I remember, the paelontologist in the original Godzilla said something about the "beast being awakened and mutated by the nuclear bombings, making him radioactive himself" or something like that in the press conference, but please correct me if I am wrong. :)

And also, if Godzilla was mutated by the bombs or not is not what disappoints me, is the message losing it's weight.

I think Godzilla's taking more of a view on nature in this version rather than just a message against nuclear war. Unfortunately when he's running around saving the world and ignoring humans to pursue the muto it kind of loses that message too, with the mutos being a better representation.

Spinojira,

The original Godzilla was said to have been "awoken" and the bombs made him radioactive. And seeing as Ishiro Honda and Eiji Tsuburaya wanted Godzilla's skin to look like it had been seared and burned, it's a good bet he absorbed amounts of radioactivity.

But it's never explicitly stated he was "mutated". Simply he was a massive, prehistoric animal that woke up from H-bomb testing and survived being showered by radioactive fallout. I always assumed his atomic breath was attributed to his exposure, but it's never really said.

In any case I think the message of having a lack of control over nature works best with Godzilla and MUTO in tandem. I recently wrote an article for Scified about this very thing and touched on why it was best Edwards kept the nuclear themes in the background. Briefly put, the nuclear themes just aren't as relevant today.

I share your opinion @DURPOO4.

Thanks, @GMAN2887! 

As far as the nuclear themes, I understand they are not very relevant today. But the message of man hurting the world the way he is, is what I wanted this movie to portray.

I don't think that was supposed to be the message to begin with. The idea was that man can't control the natural world and whatever plans we attempt to throw at it with our mass of technology isn't going to change that inevitability.