The correct answer to this open question is the following.
The single most crucial factor in selecting a cabinet member would be loyalty.
The President of the United States is the most important political figure in the nation. He is the head of the Executive branch and the Cabinet. For his Cabinet positions, he has to find the best men and women to run the Cabinet Department with the utmost efficiency and responsibility. However, due to the delicate information circulating on a daily basis in the Executive branch departments, loyalty is the most important characteristic to me.
A cabinet member has to be loyal and show it every single minute because otherwise, filtrations can cause so much damage to the presidency as we have seen in this administration. There are people inside the White House that had filtered important information to mass media outlets and the next morning, that classified information appears in the news and that information could compromise the security of the United States.