Simply consuming carbs doesn't stop ketosis. It's about how many carbs it is and how quickly they hit your blood.
You might handle 20g of vegetable carbs in one sitting without affecting ketosis much or at all. But 20g of grain or sugar carbs is an entirely different thing because they are faster.
Want to eat an apple without stopping ketosis? Eat a small one or part of one with peanut butter on it. Adding the fat slows down the sugar.

But another thing to note is that if you've been in ketosis for several weeks (assume 6 to be sure) it's really not a big deal if you're kicked out of ketosis as it will only be temporary. You'll get right back in once your body has used up the glucose. Your brain needs a minimum amount each day anyway, so you can either allow your body to produce its own or consume carbs to supply it. Either way, glucose will be in your blood for your brain to use every single day, fat fast or not.

Now, if your intention for fat fasting is to produce the highest ketones possible, it will certainly slightly lower that temporarily. But, it shouldn't have any affect on fat loss. The real benefit of the fat fast is achieving such intense appetite satisfaction from both the high ketones and the slow burning fat that you can have a day or so of very low calories.
So the potential issue with consuming carbs that affect ketosis has more to do with how it affects your appetite and ability to achieve the very very low calories