Brushed my teeth for years with this water; never had a problem!
I always brush my teeth after every meal. I use airplane bathroom water all the time. Never had a problem. I fly United. Maybe they have better sanitation. But it is simply not an issue. There are some planes which clearly state that the water is not potable, and in those cases I don't use that water.
The only time I have not used the water to brush my teeth is when the United plane took off from Shanghai to SFO. I knew that tank was loaded with water from China. I know that water is not safe to drink. But if you take off from a country that you know has potable tap water, no problem.
In fact, in some lavatories, they have little dixie cups for you, implying that you can use those cups to drink the bathroom water or brush your teeth.