Some bettas do like to eat shrimp. But I have RCS in my tanks with platys, white clouds, an oto, and danios and have never seen them eat or chase a shrimp. I also keep the fish well fed. I also have another tank where I breed shrimp, and it contains an ADF. No problems there either. I just have plenty of hiding places (java moss and cabomba) for the shrimp.
But yes, all types of crayfish will eat anything they can catch, and they can catch a lot, including sleeping fish.