Most toothpastes contain Bicarbonate of Soda.
My dental hygienist blasts my teeth with Bicarbonate of Soda to clean them.
Try baking soda instead. It can actually help if you want to whiten your teeth.
I tried it many years ago for arthritic problems and it did nothing for me. I used to drink it. I think it was supposed to be a tablespoon a day.