The way I see it, those who may be offended think...
1. Godzilla is an offensive reminder of Hiroshima and Nagasaki
Valid point, but I believe enough time has past and Japan and the west have such a close relationship that this is a stretch. In the later movies Godzilla became a good guy, and helped fight the other monsters like Mecha-Godzilla, correct? Godzilla had the same effect on western audiences that Honda had with motorcycles, one destroyed cities and the other destroyed the bike market.
2. Godzilla is a negative cultural stereotype.
If it's a negative then there should be no Japanese reference at all. What else could be referenced? Pokemon? Sushi? bad ideas...
3. It's just stupid.
hmmm, maybe your right...
I vote monster!