This section is coming soon. I need to replay the game before i can fully write up this section, however here are a few basics:
There is plenty of Racism withing Spira, however, it is mostly belief based. You have your regular, Yevon faithful humans who make up a large portion of the population of Spira. They particularly distaste the Al Bhed, however, they also have their issues with the Guado because of their superiority and isolationist ways.
Next there is the Ronso who live on Mount Gagazet and protect the sacred path to Zanarkand. They are somewhat proud and keep close to eachother, with very little need of interaction with people in the outside world [aside from Blitz Ball!]. Then there is the Guado, who are much live an Elven race. They believe that in terms of Yevon, they are superior, for they protect the Farplane and know how to manipulate the power of the pyreflies.
Last, but definately not least, there is the Al Bhed, hated by all [if not most] in Spira because of their use of forbidden machina. Many blame the actions of Sin on the sins of Al Bhed. While the Al Bhed are faithful people, they go against the grain of the rest of the world and for that are punished.