In order to live in this world and find peace and the resultant happiness which comes from that, it is crucial that we take responsibility for our speech, actions, and how we process or deal with our thoughts. We have no control over others and how they think, act, and speak, but we are responsible for our own actions, reactions, and behavior.
Real yogic mindfulness means living in an equipoised state. That my interaction with others (and the world) is driven by the recognition that I am an eternal spiritual being. “I” need to be in control of my mind and emotions rather than my mind and emotions controlling me. I don’t have to live from the default and instinctive position of feeling I must respond or act towards others based upon what my mind and emotions are telling me.
These are a few verses from the Bhagavad-gita which speak to this state:
Perform your duty equipoised, O Arjuna, abandoning all attachment to success or failure. Such equanimity is called yoga. Bg 2.48
He by whom no one is put into difficulty and who is not disturbed by anyone, who is equipoised in happiness and distress, fear and anxiety, is very dear to Me. Bg 12.15
One who is equal to friends and enemies, who is equipoised in honor and dishonor, heat and cold, happiness and distress, fame and infamy, who is always free from contaminating association, always silent and satisfied with anything, who doesn’t care for any residence, who is fixed in knowledge and who is engaged in devotional service — such a person is very dear to Me. Bg 12.18-19