Oy Vey, the Monotheist's Dilemma: If I'm right, you're wrong. If you're right, I'm wrong.
If you are right, why do you want to keep the light to yourself? Assuming of course that you believe you have been given light and are not merely engaged in some culturally intriguing curiosity.
Proselytizing is an excellent thing, mandated not only in the New Testament, but in the Tenach ("Old Testament" to you goyim out there) as well. The Psalms are full of it. Monotheism by its nature requires it, if one is to be truly compassionate. Sometimes I fear the "Thou Shalt Not Proselytize" folks are in fact closet polytheists, preferring one god among all the other "true for them" choices.
"I will praise you, Lord, among the nations; I will sing of you among the peoples." Psalm 57:9, and literally hundreds of like passages. It does not say "I will praise you behind closed doors, so no one will take offense." You may not like my interpretation, but the preference for closed doors may well come from fear of persecution, but it is my perhaps unscholarly opinion that "Closedness" has actually encouraged suspicion over the centuries and played into false and dangerous gentile understandings of what it means to be "the chosen people," i.e., some sort of "superiority" or "secretive monopolistic position" rather than a people chosen to carry a particular life-changing message of blessing for the world (the "FedEx-men of the spiritual realm," if you will).
All that said, Bachman spoke inarticulately, which was then magnified by folks bifurcating her statement hoping to make her look extra bad. Apparently the Bifurcators achieved success.
You can go on and on, as you please, but it is untrue gibberish that you are attempting to sell as fact. Jews do not proselytize. And I don't have to waste my time justifying that precept to you or anyone else.
Christianity is also the example thing, but also much more of the “go out and baptize” thing as Jesus said in the Great Commission. And I guess in the Greek it is not so much “GO” (as in going out to do specific mission/ evangelism), it is more of a “As you are going (about your daily life) be a witness and baptize and teach others to obey what Jesus said.”