I have a couple ghost shrimp with my betta in my 20gallon. The only thing I had a problem with was my shrimp cooking!!
I have very high pH and very hard water too, and those two factors have never effected my shrimp, only my temperature. My tank usually hovers around 78 - 80 Fahrenheit. I got 8 shrimp originally and only two have survived. The other six all died over the course of about 3 weeks. I would find them on the bottom of the tank bright pink and cooked through!! It seems some of them manage to adapt and some don't. Since they're only like 30 cents a piece its not costly to try until you find a tough guy. The two I have now a very active, healthy and large. They're thriving and my betta doesn't mind them at all.