Oatmeal, rice, nuts, legumes, avocado, etc. are rich in proteins. You don't need to be afraid from getting protein deficient. I haven't had animal or dairy protein foods for 30 years and still no deficiency, neither do the horses, elepehants, gorillas and human babies that get solely breastfed for the first 16 months with human milk that just has 1.3-1.6% proten in it. If you have a white coating on the tongue and/or mucus discharge in throat or chest, it is best to discontinue these products for they will just clog up your lymphatic ducts and capillary walls, and cause loss of calcium in your organs and skeletal system. If you don't have any of these systems, you are OK, but keep monitoring the tongue so as not to harm yourself.
With regard to the liver cleanse, it is easier for the liver to release stones when it is not engaged in trying to break down proteins from foods. But if that is all not agreeable for you, eat these anyway, but definitely avoid them on the day of the flush.