In his first lecture on R. Chaim Ozer Grodzinksi for Torah in Motion, history professor Marc B. Shapiro says: Some people have a problem when you have chazzanim like Dudu Fisher who sings secular music. You can cite some rabbis who say that you can use tunes from secular music in the synagogue.
“The Shulchan Aruch states that when you have a chazzan who uses curse words or he sings love songs, you warn him not to do this. If he doesn’t listen, you remove him as a chazzan. If you sing non-Jewish music, you are not qualified to be a chazzan.”
“The Mishna Brura says that non-Jewish music refers to non-Jewish religious music. I don’t know if Irving Berlin’s White Christmas falls into this category.”