Christmas and Chanukah
Cross-religion education is a good thing, and I think most people would welcome serious inquiries from people of different faiths if they want to know more (or even attend services or other rituals). I've certainly participated on both sides of that and seen no problems. But I think we should remember that our religions are separate; they have different emphases and that's ok. We don't have to agree, and we don't have to try to build a lowest common denominator.
To my Christian friends, I wish you the best in your season of holiness now under way, as I know you wish similar things for me during the high holy days and at other times. I'm not offended by your observance of your religion; you don't need to water it down. Besides, the dreidel song is really insipid; please don't feel obligated on my account.
(Mind, I would have a different reaction to celebrations in a setting that's supposed to be neutral, like a public school or a place of (secular) employment. But that's not what I'm talking about here.)
[1] Some do not see a problem with things like singing Messiah. We all draw the "worship" line in different places.
Jewish music recommendations
Oh sure, lots. :-)
For choral music, I cannot recommend highly enough the works of Salamone Rossi, a 17th-century Italian composer who wrote some gorgeous music for 3 to 8 voices. His Shabbat music has been collected as "Songs of Solomon" (yes, it's a pun on his name). There are two different two-CD recordings, both very good and findable on Amazon last I checked.
For choral performances of a variety of Jeuish music, check out the Zamir Chorale from Boston. They're very good, they have several recordings, and they have a mix of liturgical, Israeli, Yiddish, and other music.
For modern singable music, some liturgical and some not, Debbie Friedman is very popular. Her music is kind of folksy, though the newer stuff is sometimes more performer-oriented. (She grew up in the folk traditions of the 60s.) There are a number of other good performers in this space too -- Jeff Klepper, Benjie Ellen Shiller, and Danny Maseng being some of my favorites -- but I'm not sure what's out there in the way of solo recordings. I know them mostly from compilation albums.
If camp-style music is your thing, NFTY (National Federation of Temple Youth) has published several compilation albums over the years. You can get them through Transcontinental Music.
For more Chassidic-style music, which is sometimes meditative and almost mantra-like and sometimes more lively, the name is Shlomo Carlebach. He's a so-so singer in terms of technical qualities, but you can just feel the spirituality in his singing.
For instrumental music, there are lots of klezmer bands out there. I'm out of my depth there; I enjoy the Klezmatics and the Hot Matzohs, though I don't know if the latter have recordings.
I hope other people reading this will add their own recommendations!