If drawing each other closer and closer to G-d is a major Jewish objective, then driving Him farther and farther away from anyone must surely be seriously wrong … and mortally dangerous.
Indeed it is, and it’s what we do when we “profane G-d’s name”, i.e., when we who represent Him turn around and say or do anything inappropriate which thus reflects poorly upon Him and besmirches His reputation. After all, if we who profess to believe in Him and His instructions act poorly, what then does that say about Him?
So we’d all need to make a concerted effort not to be guilty of that. We’re in fact to “be very compassionate towards the standing of our Creator in the eyes of others,” which we do by “considering and reflecting upon all of our actions, and making sure that none of them lead to the profanation of His name”.
For aside from the inherent problem of having G-d, whom we love, look bad in others’ eyes, profaning His name is one of the most serious infractions of all (see Pirkei Avot 4:4 and Hilchot Teshuvah 1:4).
The point is that we must each be on guard to be the best representative of our people, tradition, and values that we can be and to reflect well upon G-d Almighty who granted them to us. But know that that’s all relevant to who a person is and what he faces.
For Torah scholars must be especially on guard about this. As Ramchal puts it, “The honor and glory of Torah comes about when the ones who study it a lot perfect and ennoble their characters …. (Thus,) those of them who do not do that cause shame to be cast upon the study of Torah itself” and profane G-d’s name.
And so the great sage Rav said that he would be guilty of profaning G-d’s name, “if (he) were to buy meat and not pay for it on the spot”, and Rabbi Yochanan said he’d he guilty of it “if (he) were to go just a small distance without reciting words of Torah or without wearing tephillin” (Yoma 86a). For “each person, according to his standing, and according to how he’s perceived by his generation, must recognize the fact that he must do nothing that wouldn’t befit a person such as himself to do” for if he is not careful about that, “G-d’s name would be desecrated through him”.
The rest of us who are not of that caliber must consider our standing in others’ eyes and take that into consideration. For while not all of us are scholars or community leaders, we each do represent G-d’s covenant and thus His reputation, and must be loyal ambassadors for the cause.