If it is truly thrush, then it can be a rare form of die-off reactions, although thrush is actually Candida in the mouth. Of course I can’t see your throat so I have no idea if this is really what it is. However, the white patches definitely sound like Candida. My theory about thrush happening during a cleanse, detox, or even the diet itself is that the Candida is being cleaned from the body and this is simply one symptom that can show up as a reaction of the process. There are other symptoms which sometimes show up during one of these periods such as access flaking of the skin or a Candida rash.
Go to Google and key in “thrush mouth” and then click on “Images” at the top-left of the page. See if your symptoms are similar to any of the photos.
For treatment, definitely read the post titled “oral thrush” which I just bumped up so it should be easy to find. This should help your situation.