This isn't what I use on my hair of course, but I happen to have a bottle of "fractionally distilled aloe vera liquid". It's considered to be an edible substance, so it has a nutrition label on it.

Anyhow, to get to the point, the nutrition label says an 8 oz serving of this stuff has <0.24g (less than 1/4 gram) of protein.

I have no idea how much of the raw gel it takes to produce 8 oz of this liquid, but one would assume it takes at least 8 oz of the raw gel. So even if you're using 2 Tbsp of aloe gel, that would be the equivalent protein amount of maybe 1/8 of that 8 oz serving, or <0.06g (less than 6/100 gram) at the very most.

So yes, the aloe gel does have protein in it, but for the amounts we use on our hair, unless your hair is super extremely sensitive to protein, the amount of protein in the gel would be inconsequentially small.
co-wash - Suave Naturals Coconut
condish - Trader Joe's TTT and Refresh
styling - FOTE, shea butter, jojoba oil, LA Looks

Kryptonite: Stearalkonium Chloride, quats