That's not what Doug Ramsey's authoritative Desmond biography "Take Five" says. Desmond did for a while believe that was Jewish on his father's side of his family, but he was wrong. The Brubeck Quartet IIRC did have to play without Desmond on a tour that took them to Saudi Arabia because it was thought that Desmond was Jewish, but Desmond's father, Emil Breitenfeld was of German ancestry.
Here's what a Washington Post article says about Desmond's ethnicity: "Desmond was born in San Francisco in 1924 and was known, until he changed his name at 21, as Paul Breitenfeld. He was often assumed to be Jewish, but neither Ramsey nor, apparently, Desmond himself could find a conclusive answer"
Whatever the truth about his lineage, if Desmond believed he was Jewish for most of his life, then In a sense, he was - because if you even mistakenly believe you are Jewish, it probably affects your sensibility and outlook on the world; for example, in terms of one's reflexive reaction to instances of antisemitism, or perhaps in feeling a member of an out-group.