Judaism isn't a religion.

 You may have heard people refer to themselves or others as "religious jews" but that is a term that only really exists in Israel. A more correct term would be practicing jews.

Here is an explanation based on things said by Rudy Rochman:

Judaism is not a religion. Let's compare it to other religions: 

In Christianity if you don't believe in Jesus and his teachings, you are not a Christian.

In Islam if you don't believe in the Quran, Surrahs and Muhammad as the last and most important prophet of God,  you are not a Muslim.

In Buddhism if you don't believe in Buddha and his teachings,  you are not a Buddhist.

But in Judaism you could be atheist, agnostic or even anti "religious" and you are still a Jew.

The definition of religion is: (1) : the service and worship of God or the supernatural. (2) : commitment or devotion to religious faith or observance.

A Jewish person can have no connection to those and still be a Jew.

So what is "Judaism"?

As Rudy put it "Judaism" is a portable "suitcase" created by an indigenous nation while being expelled from their land: Judea.

No person was called a "Jew" (יהודי) until Mordechai The Jew who was a Binyaminite and not a Jud-ite. The only people called "יהודים" (Jews) before that were the men and women of the tribe of Judah. Mordechai was part of the group of people who were forced into exile from Jerusalem by Nevuchadnetzar (y.s.v). Forced into exile I.e. Jew.

Inside the suitcase are things that help us with the following: keeping our culture, values, ethics, language, beliefs, practices, way of life, the will to eventually return to our homeland and our shared belief in higher power, all the same as those indigenous Judeans.

Although we are called a general name nowadays - Jews, throughout history we were called different names:

Israelites, Hebrews, sons of Israel, and more.

So why are we called Jews?

The Israelite nation is split into 12 tribes. And they sat together in the land of Israel. The tribe of Judah separated itself from the others to create the kingdom of Judah.  And with time the whole area came to be known under the name of Judea.  And the name of the people who originated there, Judeans AKA Jews AKA Jewish people. Because that was the last place they lived together. Some people have traditions of what tribe they come from, mostly Levites but most others were blurred upon being exiled.

Most Jews were taken to Rome on slave boats and eventually bought their own freedom. After that they split up most of them went to two places: the Sephardic Jews in Spain and Ashkenazi Jews in Germany and France. After the Spanish Inquisition the Sephardim fled to North Africa and Islamic countries. And because of the Antisemitism in western Europe the Ashkenazim fled to Poland, Lithuania, Ukraine, Russia and more.

You might see different Jewish communities all over the world but don't be fooled into thinking that this is a religion that spread to those places, instead its a people forced to go to those places because of racism. Just like in the holocaust they killed Jews because of DNA and under Muslim rule Jews were given Dhimi status because of their Jewish blood. 

It is a fact that a Jew from Poland's DNA is more similar to an Arab from the middle east than to his Polish neighbor's DNA.

The word Jew/Judaism does not appear in the Torah, the base of Jewish faith because at the time there was no Need for this culture-keeping tool. 

When our Gentile neighbors misunderstood Judaism as only a religion they considered it a religion and this way of thinking has stayed with us since. 

The Native Americans are a nation (split into tribes) that has its own beliefs and practices. And even if someone doesn't believe on the gods of their tribe they are and always will be a native American and will still have a connection to their land and their people.

This can be compared to the Druze nation in Israel who have a set of beliefs and traditions associated with their people.  Someone can be not practicing and still Druze.

So with Jews you can be unaffiliated with the beliefs and traditions bit you will always be Jewish and you will always have a connection with your indigenous homeland-Israel.