When I did my two reboots (the first one was 30 days and the second one, a few months later, was 60 days) I didn't take any supplements at all, including protein. My weight went from 365# to 200# and I estimate that 35% of my weight loss came from losing muscle mass rather than losing bodyfat. I probably could have retained more lean tissue if I were supplementing with whey protein during the reboot, but I wanted to be a purist and do it exactly the way that it was done in the film. In retrospect I should have taken supplemental whey protein. I say this because protein is important for maintaining muscle and bone mass, for keeping the immune system strong, and to prevent fatigue.
Since the reboots, I have managed to add about 15# of lean weight and to lose another 20# of bodyfat, so my body composition is about 11% bodyfat now. I shouldn't go much lower than that at my age, so I will just keep things as they are and worry about being as healthy as I can. The really good news is that my blood pressure dropped to a manageable level.
I don't think you should be too concerned about protein at this point of your reboot, unless you are an athlete. One of the misunderstandings that naysayers have about juice fasting is that they don't seem to understand that a reboot is TEMPORARY and that the person doing it is not going to reboot forever. When a reboot is over (whether 10 days, or 30, or 60) the person DOES resume a solid-food diet, and hopefully it will be a solid food diet of healthy foods.
Protein is an essential macronutrient (along with fats and carbs) and you can't attain optimal health without it, but you need to be intelligent about it too. There are 9 amino acids that are "essential" because your body cannot produce them on it's own and you need to get them from your diet or from supplements of some kind. You cannot get the protein you need from a reboot alone, so if you are in a position where you NEED adequate protein intake during a reboot, then by all means supplement with whey protein. I managed to go 60 days without anything but juice, but as you can see that is not the healthiest approach because I did lose a lot of muscle tissue also. When the reboot was over, I took steps to make sure my protein intake was good from that point on. When I say "good" I mean I get protein from fish, eggs, meat, milk, cheese, whey, etc...and not from hamburgers and pizza.
There is a lot of controversy over protein, and since most Americans get their protein from burgers, pizza and wings, then we probably get too much rather than too little. However, protein is not "evil" either. I respect veganism and if for philosophical reasons someone chooses to stay away from any animal products whatsoever (a point that I disagree with, but that is another discussion) then they can find numerous protein sources that will give them what they need without sacrificing their principles. Spirulina, for example, is a protein dense food, as are beans.
The following is from the websitehttp://www.veganhealth.org/articles/protein
"It is easy to get enough protein on a vegan diet if you eat multiple servings of high-lysine foods (legumes, seitan, quinoa, pistachios, and pumpkin seeds) each day. But there are many vegans who are probably not eating enough high-lysine foods.
Legumes include soybeans and their products (tempeh, tofu, soy milk, soy meats, etc.), beans (garbanzo, kidney, pinto, etc.) and their products (falafel, hummus, refried, etc.), peas (green, split, black-eyed, etc.), lentils, and peanuts".
So my advice to you is to wait until after the reboot is completed, and then slowly add protein sources to your daily diet. I did a lot of research, and found that (if you are not vegan) the best sources are farm-fresh eggs, grass-fed beef, wild-caught fish, raw-milk cheese, raw-milk, and beans. You can always supplement with a high quality whey isolate, too. This is basically the by-product of cheese making that used to be fed to animals until someone discovered how nutritious it was for humans too.