Karl Marx left thousands of pages of writings, including personal letters to family. In none of them is there any awareness of himself as Jewish.
His only writing on Jews and Jewishness are the straightforward boilerplate that any German Lutheran (such as himself) would understand from his Christian/secular education and social background.
He seems to have started his higher education intending to be Christian clergy.
dear jj,
No one is born a lutheran, but Marx was born a Jew.