This movie by Sheila Hayman, a direct descendant of the Mendelssohn family, digs into Felix's religion and how the family's heritage and conversions affected their descendants during the Nazi years. Read more here:

Felix Mendelssohn was a passionate Christian. He was also born a Jew. This film, marking the 200th anniversary of his birth, tells the extraordinary story of what happened, generations later, both to Mendelssohn's family and to his music, when the Nazis remembered the Jewish roots of Germany's most celebrated composer.
Growing up in a London suburb, I never thought much about my relationship with Felix Mendelssohn. I always felt a bit weird but I put that down to having a father with a strong German accent and eccentric table manners.
— Sheila Hayman