This is the shade of difference: the door of the physician should never be shut, the door of the priest should always be open.
Myriel writes this as a private rule, but it explains his public life better than a sermon. He compares a doctor’s door with a priest’s door to show two kinds of care that should never be withheld. The contrast is practical: illness and despair do not arrive at convenient times. In the plot, this idea becomes literal when his house stays open and a desperate man can walk in. The open door also becomes a symbol for a society that could choose compassion instead of exclusion. The emotion is philosophical because he is thinking in principles, not impressions. It resonates whenever someone needs help at the worst possible hour.