Although most Christian churches advocate some sort of mission to non-Christians, no Jewish group advocates a mission to non-Jews. Proselytization seems to be foreign to Judaism.
While Jews and Christians both agree on many religious issues, we disagree, and believe each other profoundly wrong, about others.
You are not practicing Judaism if you celebrate Christmas.
Even if I wanted, I cannot do anything. When they die, we always send for their co-religionists. Muslims take the Muslim's body to bury it, Hindus come and take away the dead to be cremated and Christians come and bury their dead.
My premise is that the popular aphorism that 'all religions are fundamentally the same and only superficially different' simply is not true. It is more correct to say that all religions are, at best, superficially similar but fundamentally different.
In a very real sense, Jews have to believe that Christians have missed the point about how to wait for the end, and Christians have to believe something quite similar about the Jews.
Being nice to people is, in fact, one of the incidental tenets of Christianity, as opposed to other religions whose tenets are more along the lines of 'kill everyone who doesn't smell bad and doesn't answer to the name Mohammed'
There is no Muslim version of 'love your enemies, pray for those who persecute you' or 'if anyone strikes you on the right cheek turn to him the other also'.