Final answer:
Non-discrimination is the term that describes the day-to-day duty of showing respect toward all people without regard to race, religion, or gender.
Step-by-step explanation:
The day-to-day duty of showing respect toward all people without regard to race, religion, or gender is known as Non-discrimination. It means treating everyone fairly and equally, without discriminating against them based on their characteristics. Non-discrimination is an important principle in creating an inclusive and equal society.