Place the berries and sugar into a blender. Allow to sit for 20 minutes to release any juices, then blend on high until pureed.
Into a bowl, press the puree through a finely meshed colander or strainer to get rid of the seeds. Stir into the strained puree the kefir, cream, vanilla, cinnamon, lime juice, and salt. Taste and adjust the spices and sugar if needed.
Chill for 30 minutes then freeze according to your ice-cream manufacturer’s instructions. You may serve it immediately, though it will be soft, or freeze for 4 hours to harden.
Notes
If you don't have an ice-cream maker, you can freeze the sherbet base over night, then spoon out the frozen portion and put it into a food processor or blender and pulse until smooth.