jw
Are you fasting for autophagy? Then yes, the wrong toothpaste or mouthwash could technically trigger an insulin response and break your fast if sweetened with sodium saccharin or aspartame.
Are you fasting for dietary discipline, then I wouldn’t worry about it.
(Try Burt’s Bees toothpaste that’s sweetened with Steviol.)
If the answer was yes would you stop brushing your teeth before starting your day? Fasting will be a lot easier when you lose your teeth to poor hygiene habits. Or someone punching out your teeth for stank breath.