The short answer is, we don't know, and the evidence is apocryphal at best.
What we do know is that what we believe to be his life's story -- born in Genoa, Portugal, from a family of Italian ancestry -- is based on consensus, not hard facts. Our first-grade history books only state what a few historians have agreed on might be the truth based on documents and his own statements.
Much of his life is however disputed, and these disagreements already began in his lifetime.
We do know a few hard facts:
His name -- Christopher Columbus in English, Christoforo Colombo in Italian, Cristòfor Colom in Catalan, Cristóvão Colombo in Portuguese -- was changed by him. Why or how is disputed, but there are several discrepancies as to its origins, leading many to believe he was concealing something.
In this context, both he and his son later had a tendency to push their 'nobleman' heritage of which there was little evidence beyond their own comments.
While he spoke several languages, his written languages contain rather frequent variations often bizarre in style, handwriting, grammar, and syntax. Christopher Columbus's language is Castilian punctuated by noteworthy and frequent Lusitanian, Italian, and Genoese influences and elements. One historian pointed out that it may be because his primary language was actually Ladino, or Judaeo-Spanish. Again, this has many believe that he was pretending or concealing something about his true heritage.
As was common in these days, rich people and noblemen had the tendency to have artists make paintings of themselves. It was a sign of prestige and ego -- similar to the modern 'selfie' custom. Columbus however refused to sit for artists and no known contemporary paintings seem to exist -- so we do not really know what he looked like.
His signature is cryptic to say the least. While he signed it as a Christopher Columbus at times, his most common signature actually reads Xpo-Ferens -- a combination of Byzantine-Greek and Latin that seems to mean Chrispto Ferens, 'Porter of Christ'. Above it he marked a triangular line of dots and letters, the meaning of which is unknown. It's heavily argued as to why he did that.
The Jewish Connection -- Nobody Expects The Spanish Inquisition!
Well, the Jews did.
During Columbus' lifetime, Jews became the target of fanatical religious persecution. On March 31, 1492, King Ferdinand and Queen Isabella proclaimed that all Jews were to be expelled from Spain. They were forced to either convert and become Conversos, or leave.
Or be tortured by the Spanish Inquisition. So many either left, converted or pretended to be converted. Those that were found to pretend to be converts but still secretly practiced their Jewish faith were known as Marranos -- pigs -- and particularly hard dealt with by the inquisition.
Some historians concluded that Columbus was such a Marrano, whose survival depended upon the suppression of all evidence of his Jewish background in face of the brutal, systematic ethnic cleansing.
As evidence they point to his signature which could be interpreted as resembling inscriptions found on gravestones of Jewish cemeteries in Spain, a cryptic substitute for the Kaddish, a prayer recited in synagogues after the death of a relative.
Then there are a few other strange provisions he left behind, one of which underlines his wish for the Holy Land to be liberated from the Muslims. While this was also a Christian desire, Columbus seemed to have a particularly strong desire for the city to be liberated and the temple to be rebuilt.
One thing that many also have pointed to is the date of his planned departure -- August 2, 1492 -- which just happens to coincide with the Jewish holiday of Tisha B'Av. Columbus then postponed this original sail date by one day -- was it to avoid embarking on the holiday, which would have been considered by Jews to be an unlucky day to set sail?
Also, it is believed that it was not queen Isabella at all who funded his voyage, but a group of Conversos. Letters Columbus wrote after his first voyage to these men seemed to imply that.
Why all this mystery? Was he really trying to conceal something about his past, or are these just coincidences? Was he really Jewish?
It is quite possible that they really are just coincidences. Who you were and especially where you came from was very important in the upper echelons of society.
In other words, high society was much like High School.
Columbus's ego may have tried to push his social status a bit too much, leading some to believe he was actually hiding something -- while in reality he was just overcompensating for a low self esteem.