You need to use NonUniformResourceIndex for that to work correctly, like this:

return mul * CascadeDepthsTexture[NonUniformResourceIndex(cascadeIndex)].Sample(ShadowSampler, Saturate(ScreenToUV(screenCoord)));

You need that whenever the index into your descriptor array could have different values within a wave. Nvidia ignores that hint because they calculate on their own, but AMD relies on it for correct results (which is why it works on Nvidia but is broken on AMD). If this is a pixel shader you don't really know how your threads map to waves, except that threads in a 2x2 quad are in the same wave. Since you're varying the index within a quad you know for sure here that the index will vary within a wave, so you definitely need NonUniformResourceIndex. In most other situations within a pixel shader you can only assume the index is uniform if it has the same value for the entire Draw (for instance, if it comes from a constant buffer) or if you do wave operations to force the index to be wave-uniform.

Keep in mind that using varying descriptor indices + NonUniformResourceIndex can make things more expensive. GPUs will typically “waterfall" when this happens, which basically means they will do N texture fetchs to handle however many different values of the index occur within a wave. In your case it means your shader will sample from both cascadeIndex == 1 and cascadeIndex == 2, and then select the appropriate result, effectively doubling your texture fetches. You could potentially avoid this by using a Texture2DArray instead of two separate texture descriptors.