All neos can breed with each other, they are all the same species, just different colour morphs that have been selectively bred for. If you allow two colours to interbreed you'll mostly get the wild form, which is brownish or near colourless and not very interesting. You are not likely to get any more genetic issues with cross bred colours, probably fewer actually. All the colour morphs are at least somewhat inbred now, and that is what usually leads to genetic issues like deformities.
It has been done, many times. If you want different colours, best to start with the wild form and isolate the colours you want and breed them, cull the ones that don't have what you want. That is how all the colours were isolated in the first place. It began with wild cherry shrimp to start with and crossing colours will return the offspring mostly to their ancestral colour.