This verse from Bhagavad Gita Karma Yoga simply means “be yourself”. Follow your Dharma (the idea of what you ought to be and do), not to be confused with religion, the closest meaning of Dharma is the nature or tendency of something, for example, Dharma of water is to flow, to be colorless etc. Be true to your idea of who you should be. Don’t try to be what someone else is. While you may be an excellent pretender, there will always be fear in your heart.
Engaging in one’s own duty, one possesses the correct inner mentality to accomplish it, but for engagement in another’s duty the correct inner mentality would not be present even if the external action was performed perfectly. The worry (or indecision) and questions regarding some aspect of other’s duty would lead to inner conflict which is very detrimental for one’s consciousness and atma tattva or soul realization.