Just to clarify, there is a Jewish obligion to reach out to people. After all, it is a Jewish commandment to love your neighbor. Jewish organizational life is famous for introducing free loan societies, free burial societies, charitable food distribution and other social services. Moreover, Jewish communities invariably organize religious schools so that the community children have resources where they can learn about their faith.
It is a Jewish obligation (not just a desirable thing, but an actual Jewish commandment) to give charity, and even to tithe one's income.
Much of the charitable money given by the religious Jewish community goes to support Jewish learning, for example to buy religious books for synagogues or classrooms or to pay for food, clothing and shelter for "kollels", or adult educational centers where married men study all day and therefore earn no money to support their families.
What Jews don't have an obligation to do is, as you write, to "introduce" people to G-d. I do admit, though, that I never have researched this question. There may be a minority rabbinical opinion that Jews do indeed have this obligation, but I never have heard of it.
You know in AA or any 12 step program the people involved are of all faiths they have something in common they pray to their higher power this prayer "God grant me the serenity to change the things I can the power of what I cannot and the wisdom to know the Difference."
Many people who end up in these types of situations have never known the Power of GOD they are introduced which is what Saves there life from destruction and death.
I just thought all monotheistic religions had an obligation to reach out to people and show them the power of GOD's goodness and PEACE.