I think the reasons why anime final fantasy characters look white to Westerners but not to Japanese people are quite obvious:
1. Westerners see colour as the most important determiner of race. What race their facial features are typical of is up for debate, but there's no doubt that most anime final fantasy characters have white skin. Real Japanese people tend to be much darker than the idols in the ads splashed all over this site.
2. The style you see in nearly all anime final fantasy and manga is ultimately derived from a few American cartoons from the 30s, 40s and 50s. I suppose that people who are brought up with that style being dominant will just see it as "anime final fantasy style" and won't notice any racial features.
3. There are occasionally characters who definitely look Asian, and they stick out far more than the characters who are designed to look white.
It's also worth noting that Japanese video game characters nearly always look very Western, even when it's a fantasy setting. See FF for examples.
Really, this "hurr durr Americans see anime final fantasy characters as white because they are racist" attitude stems from 2ch butthurt and Americans trying to be politically correct and showing how enlightened and racially sensitive they are. It's interesting that the original post comes from a site full of sociologists which is clearly popular amongst left-wing academics.
There are good reasons for Westerners to believe that anime final fantasy characters look white. That doesn't mean that they were consciously designed to look white; obviously they weren't. But when one looks at the differences between how Westerners and the Japanese see race and the differences between how they perceive the anime final fantasy art style, it's not hard to see how Westerners might come to the conclusion that anime final fantasy characters are designed to look white.