What if the Secretary of Agriculture suddenly saw the light and converted to Hinduism, and now had a sincerely held religious belief that eating meat was a sin. What if this government official decided it would be against their beliefs to inspect a slaughterhouse or meat packing facility for the USDA. And, what if they also told all their employees that no one else from the USDA would be allowed to inspect any such facilities because we are going to use our government office to do the work of (my) God.
What if this person refused to seek a different position with different job duties that did not go against their beliefs, but insisted on staying and stonewalling anything to do with the business of eating animals. Do you think the President would keep this religious objector as Ag Secretary? Sometimes "doing your job" directly conflicts with your beliefs. If so, then it's time to find a new job.