My experience is that the louder places shout about a GF product, the more rice and maize flour there is in that product and the more stabilisers, bulkers and added ingredients it has.
on the other hand, lamb and chicken should be GF - unless mucked around with, minced up and stuck back together.
Our local kebab place does the most gorgeous lamb and chicken. Diced, cooked to perfection, tender, juicy, with lovely golden crispy bits. I just ask them not to put it in a pitta. Never had a problem with gluten from it.
They also serve fab chips, also un-glutened, but those go down Mr B’s hatch.
so that means it hits all my spots - We can both eat enjoyable food from there, and mine can be low carb, GF, and carni