It was important that Ezekiel understood that those who were serving the people by having the responsibility of the sacrifices and entering the holy of holies disrobe their attire that they use to approach the Lord and put on other vestments as they interact with the people in every day settings. Interestingly enough what I wear that first service, my robe, I do not use in every day settings. I only use my robe for Sunday morning, weddings, funerals, and any other services where I am asked to be present in a way that I am invoking the name and the presence of the Lord.
We have a completely different theological approach to our understanding of the presence of God. We do not believe that God resides in a single location but rather that God is present with all of us at the same time. We do not believe that any individual has a closer relationship to God because of their earthly responsibilities. No matter who it is who wears the robe, they do not have a special "in" with God as opposed to the mechanic who busts his chops every day in the shop. That is part of our Calvinist approach to our faith. God loves us all...equally, and we all have the same access to God. I like that.