Yes, you are correct. The Al Bhed are the villains of Spira. They destroy religious statues, sabotage religious rituals, and bring death and destruction to Spira. There will later be a side quest where you can bring a holy genocide upon them all. This unlocks a secret ending, where Tidus becomes an official Crusader of Yevon.

Don't believe me? Then play the game and find out for yourself.