In Buddhism, we are taught something similar to minding our own business: don’t pay too much attention to other people’s karma. We can so easily get caught up in judgment about whether others are living the way we think they should or practicing the way we think they should. This is a waste of time. Of course, the phrase mind your own business can be misused to rationalize away situations where others need our help or understanding, but it does remind us to avoid getting lost in our judgments. Others have the right to do things their own way. They have the right to make their own mistakes. When appropriate, (and it is appropriate far less often than we think), we can offer a gentle hint of advice, but other than that we should stay it is generally best to stay out of their affairs.
At the same time, the more obvious meaning of the phrase is often ignored. Minding our own business also means, take good care of your own life, your own affairs, your relationships and your possessions. Watch what you feed the body. Watch what you feed the mind. Get your oil changed on time and file your tax returns and so on. Mind all this with care, with mindfulness and attentiveness. In this sense, mind your own business is an important teaching.