I’m an ethnic Jew and through Jewish Law I am a Jew (my mother was raised Catholic, but her mother was Jewish and the rest of that side of family is Jewish). I was raised Christian and am extremely devoted, but the Jewish side of my family is extremely important to me and highly influential in my life. I’ve seen several people asking a similar question but no one has really been able to answer with my details. Here is the necklace I have ordered; https://www.etsy.com/listing/579014913/star-of-david-with-cross-necklace-cross?ref=yr_purchases Thank you!
I think it is fair to say many Jews would find it distasteful or offensive (I certainly would). The cross has been used as a symbol in Jewish massacres for centuries (e.g., during the Crusades). Beyond that, wearing both symbols together appears to equate both religions even though their belief systems are fundamentally opposed.
Whether it is permitted by Jewish law might be a matter of dispute. R Ari Enkin brings an opinion forbidding it (here)
R Menashe Klein was once asked by a doctor if he could wear his hospital-issued coat which includes a cross as part of the hospital’s logo on the front of the coat. He responded that the permissibility of wearing such a coat depended on the purpose of the image of the cross. If it has religious significance, then it would be forbidden.
There appear to be other perspectives brought in this related question.