For the most part, traditional sourdough bread is made with just 3 simple ingredients; flour, salt and water. So if the bread in question is the traditional simple sourdough bread, then it it is definitely vegan friendly.
4 Things to Check Before Purchasing Sourdough Bread
Enriched Sourdough Bread Could have Non-Vegan IngredientsBread Tins may have been Greased with Non Vegan IngredientsSome Sourdough Breads are Sweetened with Non-Vegan IngredientsSome Sourdough Starters are Given Non-Vegan Foods to Boost Their Activity
Going through the ingredients list is the best approach when buying shop bought sourdough bread. Check for common non-vegan ingredients such as eggs, milk, cream, or butter.