Because sourdough bread (like all bread) contains grains, it is not gluten free. However, it contains far less gluten than other kinds of breads. This is because the bacterium that causes sourdough bread to be formed breaks down the gluten in the wheat, which is something that the yeast found in other kinds of bread does not do.
How to find sourdough with less gluten
One of the biggest reasons why modern sourdough bread contains gluten is that it is not left to allow for the bacteria to eat if for more than a couple of years. This means that the bacteria have not had enough time to devour the gluten in the bread dough.