It's not just Final Fantasy; a lot of Japanese games specify their characters' blood types. The Japanese, for a little while, believed that your blood type determined your personality. This was basically a hoax to try and set up the most common Japanese blood type as the 'best' blood type.
I don't think anyone puts any stock in that theory anymore, since it was so quickly shot down by the scientific community. But it's still an easy shorthand for Japanese players, who would know the personality it indicates even if they don't believe in any correlation in real life.
Think of it as sort of like if Western developers started indicating every character's astrological sign. Of course, that would deny them the use of the ever-popular 'unknown' type, which isn't as impressive since they just don't know their birthday. Or maybe they could say the mysterious characters' sign is Ophiucus?