Has it changed its approach in the last few years? It used to be that all they did was stand on street corners and hand out leaflets that explained how Jesus fulfilled the Jewish prophecies of a Messiah. They answered questions, and put up with a lot of abuse from people who didn't understand what they were doing. They were accused of being "traitors" to their Jewishness.
But, if I recall correctly, Jesus was a Jew, preached and taught to Jews, lived in a Jewish world, read the Torah in Jewish synagogues, and died as a Jew.
It's rather hard for Jews to understand. Perhaps its just the name. They are not "Jews for Jesus", they are Christians for Jesus. Mort "Moishe" Rosen, the founder of Jews for Jesus, is a minister ordained in 1957, who has led Christian congregations. This is not a Jewish group. So why the word games? Very silly, but I guess he must have had a history in marketing beforehand. I have no problem with it, and don't understand the nasty replies, just trying to explain why some Jews get so irritated with JFJ.