Answer

Maybe it is well known to you. To me, it is not. What I do know is that the Sages write this, but I do not know that it actually holds true. On the contrary, I know fairly well that it does not hold true.
If I wanted to defend the words of the Sages themselves, I could perhaps argue that going to do a commandment provides protection, but that this is not absolute protection. If there is some other reason that he should die, then perhaps he will die. The Sages also say that because of the sin of vows, a person’s children die, and also that one who is careful with wine for havdalah will have male children. There are those who are not careful about vows and their children do not die, and those who are careful and their children do not die. There are those who are careful to make havdalah over a cup of wine and do not have male children (like the Chazon Ish, for example). Rabbi Elchanan Wasserman asks all this and explains that the intent of those sayings is that havdalah over a cup of wine helps one merit male children, but if there is some other reason, then perhaps one will not merit them. For example, if you make havdalah over a cup of wine but have sinned in matters of vows — then instead of giving you male children and killing them, perhaps you simply will not receive them at all.
If that sounds to you like a forced explanation, I suggest you read my article on ukimtas, and you will see that it is not forced at all.
So why does it not seem to me that the Sages are right here? Not because reality proves otherwise, but simply because there is no reason at all to assume that this is in fact the case. There is no indication of it, and I do not see where they themselves could have derived it from. Therefore I assume that as long as nobody has brought me proof, it is probably not true. So why did they say it? Maybe in order to motivate us to perform commandments and not fear the consequences. Maybe they really thought so and were mistaken. And maybe I am the one who is mistaken (that is also a possibility, of course). Remember that they also sometimes qualify these statements (for example, messengers of a commandment are harmed where the danger is definite), and therefore always leave room for excuses.
As for those who do outreach, I do not make a habit of defending them. You should ask them. They are biased and present things in a distorted and tendentious way, exactly like the atheist “outreach in the other direction” people.