Two of my co-workers, both women, are practicing Jews (one, B., with a Reform and the other, L., with a Conservative congregation). In addition, the husband of the co-worker who is with a Reformed congregation (S.) is a very erudite man, a walking encyclopedia of all things Jewish, and he often preaches at their synagogue on Shabbat. All three of them - B., L., and S. - know that I am an Orthodox Christian. I am friends with all three of them in real life, plus I am friends with B. and S. on Facebook, and we sometimes exchange messages about our respective holidays.
I learned a lot from them about Jewish holidays, and I hope they learned something from me about our Orthodox holidays and about Orthodoxy in general. They never seemed to be bothered by my messages about things Orthodox (in sharp contrast with my atheist FB friends who sometimes make scenes and virtually scream at me that I am bothering them with my "religious propaganda cr*p").
Once, I had a pretty long and very interesting, very peaceful and very informative exchange via FB with S. It was initiated by his message to the general, public FB page, in which he quoted some rabbi saying that the Temple of Living God is each of us. I sent S. a private message, saying that it is so striking to me how much we have in common in this regard, and quoted and explained (to the best of my ability) verses like 1 Cor. 3:16-17, 1 Cor. 6:15-20, 2 Cor. 6:16, and John 2:19. S. seemed very interested and expressed his gratitude.
I agree that arguing with faithful Jews, trying to prove something to them is not a very good idea. On the other hand, listening to them and sharing with them something that we can simply narrate about our religious life may be a resoable and fruitful approach.