Are there any hash functions/stateless RNGs that do not use XOR, but produce good quality visual randomness?
Found a solution here, as glsl, which at one time had near exactly the same restrictions I wanted:

float rand(vec2 co){
    return fract(sin(dot(co.xy ,vec2(12.9898,78.233))) * 43758.5453);
}


or as I implemented it: $\operatorname{mod}\left(\sin \left(a\cdot 12.9898+b\cdot 78.233\right)\cdot 43758.5453,\ 1\right)$