I have red cherry shrimps with my current betta, he ignores the adults. I put three shrimps, 1 female 2 males, in the tank with my previous betta which was very laid back and he didn't notice them. At every water change i had to rescue baby shrimps from the bucket and the population increased. When that betta died and I got the current one, I stopped finding baby shrimps in the bucket so presumably he eats them even though he doesn't eat the adults.
Several years ago, I managed to get a woodlouse in the tank. The betta I had then chased it all over the tank and only stopped when it lay motionless upside down on the bottom of the tank. I would not have been able to keep shrimps with that betta.
Every betta is different.