It also doesn't help that white is also the absence of pigment so a black and white manga character or a simple stick figure is just going to appear white due to the lack of shading in the drawing. White is just a terrible word to describe people of European descent.
As for a serious answer to this topic, I don't associate the FF characters with being white or Asian or any other race of Earth since those areas don't exist in the FF worlds. They are whatever race exists in that world. Some of them are different races in that world, some of them are the same. Different races of homo sapiens has never really been the focus of FF and the racial tension in those games tends to be more between very distinguishable groups (Espers vs. humans, whatever race Zidane was vs. humans) where skin color or facial features have not been a factor.
I will say that I was thrown aback in FFX at first when Tidus and Yuna had very distinct Asian features, particularly in the FMVs, but that was mostly due to my lack of exposure to Asian people up until that point and that graphics didn't really allow for that kind of distinction before then other than having the token black character. I don't feel that way any more and I appreciate when Japanese games actually feature characters that look Japanese and don't hide the fact that the game takes place in Japan. It's not weird when Americans do it so it shouldn't be weird when anyone does it.