So perhaps the answer might be: "Do you need to decide now?" Can you put it on the back burner, research it further, and make up your mind later?
I'm not going to condemn the programme, but it sounds odd to me. I mean: what is avoiding the "animal protein" about? I could accept that low protein for a short time might work for some conditions—and since animal products are a good source of protein, it's difficult to go low with those. But why the expensive powder? Why not a mix of plant foods that supply all the amino acids, as cultures that can't afford much real protein do?
And why rule out animal fats? Maybe there's a rationale for that, but what is it? Frankly, I regard most vegetable oils as pretty toxic, and I'd take some convincing to eat them. And having said that the fats and oils must be plant-based, why do these people tell you you can't have coconut oil? Is it because they think saturated fat is bad or something? Or only bad for this condition? If so why?
If it's just about elimination of potential allergens then why on earth is the selection quite how it is? Some hospitals used to use what they called a "Stone Age Diet" for that purpose (maybe still do). AFAIK, that was lamb and some vegetables.
Maybe it does work in practice and a month on some regime isn't too long.
Maybe read up a bit first and see what the latest work is suggesting about thyroid conditions—e.g.: