Attacking ignorance that is justifiably based on skepticism based on ample evidence of bad character is not entirely unwise.
And there is plenty of alternatives to toothpaste. What matters more is the brushing. Oxidation also doesn't hurt, since it reduces bacteria levels.
I was told, even, by a medical trainer who was teaching me how to perform body piercing safely, also, that according to medical science, when cleaning yourself to reduce spread of bacteria and other muck, simple friction is the most important thing, followed by blood warm temperature which melts many fats and is not hot enough to make proteins denature and encapsulate bacteria against further efforts to dislodge them. That's also why dish washers mostly are based on using sodium carbonate at around 45 degrees C because at that temperature, fats are melted, and the proteins are more vulnerable to hydrolysis.