Speaking as a Jew (one that actually was born one and practices the religion)
.. JUDAISM is a religion. Being Jewish is belonging to an ETHNIC GROUP. More specifically in a traditional understanding and ethno-religious group. So with that ethnic group comes a history of a particular religion. A person can certain be a Jew though and not adhere to Judaism.
But it certainly is a fact that Jews can belong to ANY race. But it's not uncommon to hear the phrase.. "The Jewish race"..even among Jews.
There isn't one hair type that is inherent to Jews though dark curly hair used to be something associated with Jews as a typical trait until more European Jewry came to the forefront.