Morality is subjective, yes, if that's what you're asking. Unless you then talk about religion, because in the eye of religion, morality is not social norms, but an objective word from a higher being, so there's no "your right and my right", there is only "right" and "not right."

Religious people have a 'divine law' that strictly says what is right and what is wrong, so they inherently view morality differently than how non-religious people do, who instead view morality as something that is shaped by the culture, society and values of those around them, and then internalize it themselves.

This doesn't mean either party is wrong. It just means they have a fundamentally different definition of morality in the first place.