The distinction between the religion and racial connection will be very evident when you try to apply for residency in Israel and you are asked to prove from your heritage from your mother's lineage. You can be as Judaic as an Orthodox Priest but they still will not grant you residency.
Keep in mind the many black people around the world, talking specifically those who you could easily identify as being of the continental African group and yet whos DNA is so intermingled with other groups that no link can be found to Africa at all.
Even today they have been digging up Chinese tombs whereby the remains have blonde hair, blue eyes and fair skin and yet whos DNA does not match Chinese and who's DNA does not match European and yet these were a major group of Chinese continental people.
Many people in the UK identity as Celt. They follow the Celtic language, religion and have existed in primarily Celtic regions of Ireland and Western England for centuries and yet their DNA does not trace to the Celtic home land of Austria and then France.
Take the Hittites who tried to take ove ancient Egypt. For many years they were thought to be a race or common racial group that invaded from foreign lands when in actual face Hittites were not linked by any other thing except by being a group of people whos trading capital existed in the Nile Delta, who were a mish mash of all different peoples from all over and who eventually rose to power by taking advantage of Egypt's internal divisions, and yet today many still think of the Hittites as a race group. Anyway food for thought.
It's such a vast subject. I'm no expert just more interested in History and just pick this info up along the way.