is jewish a religion or a race?

You can convert to Judaism, but Jews are often characterized as more of an ethnic religion, divided into Ashkenazim, Sephardic and Mizrahim.

Then of course they also had Sammy Davis Jr. Don't forget about him.

Neither. Most Jews aren't religious, and there is no such thing as a Jewish race. So it comes down to if you call yourself one or not, based on your ancestry.