I'm not saying there's a correct way, but American English speakers have several very distinct ways of pronouncing the word. I'm somewhat trained as a linguist, and I have a half-decent ear for hearing subtle changes in pronunciation. I kept hearing something different about how some people say "Judaism," but it literally took me five years to figure out the difference. I guess that means I'm not a very good linguist after all :(
The simple difference in which syllable people stress makes a very different sound. It's not quite as striking as the difference between "advertisement" in American English versus British English, but certainly there. It's also the same kind of difference, "ad-VER-tiz-ment" and "ad-ver-TISE-ment" (AD-ver-tis-ment is also correct for Americans.) If you don't know what I'm talking about, check out this educational video.
Now I want to know what creates the difference. Maybe I'm saying it with a Southern accent?
Apparently I'm on Team JEW-day-ism. What about you?