Last time I did the master cleanse I incorporated a teaspoon of raw sesame oil in the morning and in the evening. My herbalist recommended this me as he does this himself. He has done cleanse about 8 times and found the oil to be beneficial.
My personal reason for the oil is that I felt like I was getting extremely dry for the first part of it. The oil helped dramatically. I didn't find that it halted the cleansing process. I found it to be soothing and lubricating to my entire digestive tract. I have a lot of digestive issues including internal scarring from hernia operations when I was very young among other things, so I do feel it was a tonic for me in my case.
Ask yourself what you need. Your intuitive body will tell you if the oil is something you need to add or not.
I don't try to get too religious about anything. There's not a lot of flexibility in the frame of mind if you know what I mean. Keep it open, keep it real. If the straight and narrow path is called for, then by all means stick to it.