Can male Bettas live with red cherry shrimp or any type of shrimp? If not, what fish can?
It depends on the betta. Mine does all right with the adults--they're too fast for him, and he doesn't like hunting them if he's kept well-fed. As far as I know, he doesn't actively hunt the shrimplets, but he does eat them. However, my betta is extremely peaceable; I've never seen him flare once, and I've had him for 18 months.
All fish are hit and miss with shrimp aside from the one and only true 100% shrimp safe fish, the otocinclus. Any other fish can and will eat shrimp, especially babies if given the chance. Now with that being said, many people, including myself keep fish and shrimp together. As for Bettas, from what I read they are maybe 50/50. Some other fish that are usually a little better off are smaller fish like neon tetras, small rasboras, some guppies, and smaller plecos like the bristlenose pleco. There are a few others that some will say they have good luck with, but its random, others will say they murdered their entire colony. What really matters and helps out is how much cover, hiding places, décor, and plants you have. The more the better. Plants like mosses, subwassertang, hornwort, etc really help for babies to stay alive as they can hide and forage inside the moss like plants with fine leaves. The more "jungle like" you can get your tank the better. As most shrimp are very quick and can dart away provided there are spaces to dart away towards. Your best bet with a Betta would be ghost shrimp. They are larger, and harder for the betta to see and stalk. If they do get eaten well then your Betta had a healthy, natural, and cheap snack as they are only usually $0.30 each or so. Get 2-3 and see how it goes. I personally have 15 neon tetras, 1 bristlenose pleco, with my large red cherry shrimp colony in a 40 gallon tank. But I have a ton of plants, rocks, and décor to hide. Even regular gravel works well, as the really tiny baby shrimp can go down into the cracks between the pebbles. My shrimp colony breeds like crazy and does very well. I'm sure the neons eat some babies when they can find them, but not enough to put too much of a dent in the colony.
As Dolfan says, it really depends on the Bettas temperament whether he'll tolerate the shrimp. If you do try it add the shrimp first, or take the Betta out while you add the shrimp & give them time to find hiding places before putting the betta back, or he may think you're offering him some tasty snacks.
So super small fish like harlequin rasboras, galaxy rasboras or any of those 1/2 inch to 1 inch fish?