A "race" is an event. For example, The Annual Cross Country Race. It is a concrete noun as such.
If it's used as an action, such as a competitor trying to "race" to the finish line, it's a verb.
Fishing in a tidal "race" (fast flowing water) it's a concrete noun again.
If "race" used to refer to people by characteristics, one might argue that it becomes an abstract noun because of mere speculation about people's characteristics. You cannot see and touch characteristics.