Conversos (Marranos)

I am from Mexico and my ancestors trace back to the Conversos. (We don’t use the common term “Morranos” because of its negative connotation in Spanish, which means swine). We trace our ancestry all the way back to the Spanish inquisition. Although for many generations my family has attended church and lived in Christian communities, they always have lit candles Friday night (in a secretive way) and some other Jewish customs. I recently have become more involved in traditional Judaism, and it has been suggested to me that I undergo a conversion to Judaism. I find this very offensive, as I am very proud of my family history and roots as a Jew. What is the correct thing to do?