Rather than a blanket term like being a "purist" which can indicate a "blind faith" or being dogmatic think of it in term of common sense. The natural state of the body is one of health and that state get impeaded by the build up of toxins from a infinite number of sources. When you are fasting you are trying to eliminate these toxins so the body will heal and rebuild and work more efficiently to maintain this natural state of health.
Adding an unkown into the mix can be a waste of time cause you would probably pee most if not all of it out. Then there is the issue of adding something that can hinder this cleansing process that you are trying to achieve. Folic acid doesn't exist in nature as an independent substance and at the very least an educated guess is that it needs other components to buffer it's absorption. There is not much in the lemonade to act as a buffer an in addition you are introducing a solid that the system will hafta process and digest which will works against the main working principle of fasting which is to give the digestive system a rest. Other than critical precribed medication I would say stay with the known and allow the cleanse to works it's mojo at maximum efficiency and save the FA for after you are done.