When someone causes a great insult to the Inquisition as a whole, such as through an extremely rude and thoughtless comment or outright denying the Inquisition's way of Life, they are Shunned by the people of the Inquisition.
To be shunned means that you effectively do not exist. Those of the Inquisition will ignore your words, not speak to you, or even look at you. You may as well be invisible. The only exception to this is the Department of Atonement.
This Department provides a Shunned with a rather time-consuming opportunity to Atone for their transgression and be Shunned no longer. A large amount of paperwork must be filled out, and the Atoner must be granted audience with the Atonement Officer of the local area to verbally apologize and seek Atonement.
There are, however, extremely rare cases where a Shunned is denied any and all opportunity of Atonement. This decision is not made lightly, and is only enforced for matters such as murder. This Eternal Shun is reserved only for outsiders, as Murderers and the like within the Inquisition are often imprisoned or given an entirely different (and much less pleasant) version of Atonement (see Military Sects - The Atoning in the Species Codex).
This Shunning should not dissuade people from pursuing alliances, relationships, or trade with the Inquisition, as the Inquisition is truly quite reasonable in almost all cases.