The official FAQ says:

Leaving a Casting Career

If a character chooses to leave a priest or wizard career, mechanically he does not lose the ability to invoke blessings or cast spells. However, he does lose access to the corresponding Faith or Order specialty card if his current career does not have the appropriate
socket to hold the specialty card.

If the character has the proper skills acquired or trained, favour/power can still be generated and blessings/spells can still be performed – just without the benefit of the ability granted by the Faith/Order card.

From a setting standpoint, such a career transition is highly unusual. Leaving an established Empire Cult or the Colleges of Magic would meet with suspicion, questions, and possibly persecution. A wizard leaving the sanctioned and approved Colleges of Magic could well be branded a hedge wizard, sorceror, or dangerous renegade and find himself targetted by zealous Witch Hunters.

But 2 things come to mind.

1. Can a character go from being a mage, and turn to follow a god, and become a priest?

2. Why couldn't a character still be considered "Still a Wizard of the Order" but dabble in other things as long as it makes sense? For example, let's say I have a Grey Wizard, who is out traveling the lands, with permission from his Order of course, and during his travel he transitions out of initiate Career, say to investigator, and then back into Initiate? To all outward appearances the character never left the order, he is just not practicing as much as he should, with all this time spent investigating. Rules wise, he takes a detour into investigator before going to Acolyte.

I think in most cases you would just pick up non career skills to do the same thing, but I don't see why as soon as you spent a point in another career, everyone around you suddenly goes "WTF" like they magically know you left your Grey Order.