Fairness: a big responsibility
This is really important.
Labor unions are required by law to represent all workers in the unit fairly and completely. This includes non-members as well as your union members. It's legally known as the duty of fair representation or DFR.
Of course, you don't need to be told that you must represent all workers fairly regardless of their race, religion, nationality, age, gender, sexual orientation, or disability.
You may find that you have to represent workers who oppose the union, as well as those who are unpopular, difficult to work with, or who create discord in the union or the workplace.
No matter. Fair is fair. This doesn't mean the union can't lose a grievance or make a mistake. It does mean that every action you take must be free from bias or the appearance of bias:
That's why it's so important to keep records of your activities as a steward including phone calls, interviews, letters, contacts, and decisions. Without documentation, it's far more difficult for your union to defend a DFR case if one should occur.