While bread made from white or whole wheat flour is high in FODMAPs, traditionally made sourdough breads made with these flours are low.
Research Brief: Sourdough Rye Bread
Rye is a high FODMAP grain. While authentically prepared, slow-fermentation sourdough bread made from wheat and spelt are low in FODMAPs, sourdough rye breads tested so far in the FODMAP lab at Monash University are high in FODMAPs. But there may yet be hope for sourdough rye bread lovers.