If Judaism is inherited from your mother, it's a race. Judaism does allow people to convert, though.
Huh? Judaism is a religion, plain and simple. While the religion defines itself as matrilineal, there is no concept of racial purity, so you're talking tosh. As you say, you can convert in, but you can't convert out. there's no escape. It's not unlikely that by that standard a substantial proportion of the world population are Jewish, by that reckoning, making it irrelevant.
Looking at a definition a race is "a grouping of humans based on shared physical or social qualities into categories generally viewed as distinct by society" or "a group of people sharing the same culture, history, language, etc.; an ethnic group". So while it would then be accurate to define Jews as a race, Judaism isn't.