If I was hearing the phrase mind your own business for the first time w/o any associations I would think it meant take care off your own affairs.If I was hearing the slogan” Live and let live” for the first time” I would understand that it is a wise and wonderful suggestion to really be alive. I can not mind my business if I am minding yours but the primary suggestion is focus on your self and the slogan primarily suggests to be as alive as you are able.
I love the line “You only have one life to live. Let it be your own”.To be alive and be fulfilled to me is interacting with another person.
George Caywood 