Here’s what live and let live means to me, and what kol yisroel areivim ze bazeh means.
First: Part of the mehalech of tochecho done properly, according to some of the most machmir of posters here in other threads,is that it can only be be given to someone who is receptive – SO – until and unless you know your nosiness and interference is going to be appreciated, you have no halachic right or obligation to give it. So live and let live.
Second: As has been said above, your chumrah is not necessarily his chumrah, and your (or your Rov’s) interpretation of halocho is not necessarily that of him or his Rov. SO why would one make an assumption that you know better, or that your Rov “trumps” his? That is arrogance, and arrogance has no place in Yiddishkeit. So live and let live.
Third: As it says in Avos, have you walked in his (or her) shoes? Do you know if he or she has asked a shailah about what you are seeing? Often poskim – chareidi poskim – are makil to extremes if the particular circumstances dictate it. Do you know if it is their particular challenge, and your rebuke will do more harm than good? If you don’t know, how can you take the risk of pushing someone (further) away from yiddishkeit? So live and let live.
OTOH, what are your responsibilities? If you see something that seems to you to demand a response, perhaps your response should be one of love and achdus. Perhaps you can offer the individual a helping hand, a favour, a smile, a shabbos lunch, or simply an opportunity to talk. Perhaps you could call the person to wish them a good shabbos every couple of weeks instead of crossing to the other side of the street when you see him. IF the person get sin trouble with the law, help and advocate for him. If they need a loan or a job, work to make it happen. If they need help getting their kids into a school, or paying for it, see if you can raise funds for them. If they are sitting shiva, cook for them. If they need a place to live, don’t shoo them away because they don’t meet your standards of tznius, find a way to welcome them into the community, and show them the beauty of a tzniusdig life. THAT is kol yisroel areivim ze bazeh.
Unless, of course, to you, kol yisroel… is a sham, and what is important is maintaining your holy exclusivity and looking down on di andere….