I believe that those who say they are Jews but are not are Ashkenazim.
See chart at link below.
Ashkenazi

The Ashkenazim, aka The Thirteenth Tribe (1976) is a book written by Arthur Koestler. He was convinced that if he could prove that the bulk of Eastern European Jews (the ancestors of today's Ashkenazim) were descended from the Khazars, the racial basis for anti-Semitism would be removed and anti-Semitism itself could disappear.
The Thirteenth Tribe - Wikipedia, the free encyclopedia

However, given that 90% of those who identify themselves as Jews are Ashkenazim, including those who settled in Israel (every Prime Minister of Israel since 1948 has been an Ashkenazi Jew), the legitimacy of their claim to the Holy Land has been called into question. Koestler's book stirred up much controversy. In 1983, Arthur Koestler and his wife were found dead at their home in London. The cause of death was reported to be suicide.

The most wealthy bloodline in the world bar none and the leader of the Ashkenazi Jews in the world today is the Rothschild family. As you will see in the timeline, the Rothschilds have obtained this position through lies, manipulation and murder. Their bloodline also extends into the Royal Families of Europe, and the following family names: Astor; Bundy; Collins; duPont; Freeman; Kennedy; Morgan; Oppenheimer; Rockefeller; Sassoon; Schiff; Taft; and Van Duyn.

However, these are not the only bloodlines to worry about. You are probably aware of the centuries old practice undertaken by many Ashkenazi Jews whereby they would change their name, in order for them to appear part of the dominant race of the country in which they lived, so as they could obtain influential positions in that country, which they would then exploit to serve their real masters elsewhere. Furthermore, the Rothschilds are known to sire many children secretly that they can put into positions of power when required. Hitler was believed to be a Rothschild ''love-child.''
Timeline of the Rothschild family

The Ashkenazim comprise a large portion of ''the 1%.'' They control much of the global economy and the mainstream media. As I write this, entire families, corporations, economies and even nations are being loan-sharked in a cut-throat game of Global MONOPOLY. Goldman Sachs' Lloyd Blankfein calls it ''God's work.''

Draw your own conclusions.