Putting my chemist hat on for a moment, I would say no for the estradiol itself. Looking at the structure of it, it won't be causing any major PH balance issues or feed bacteria. It's a multicyclic carbon structure with only two hydroxyl groups to make it interesting. Basically it's about as inert for your teeth as one can imagine, and there is very little of it in each tablet.
That said, the fillers in the tablets are the thing to look at. Looking at the ingredients for Estrace tablets (the others are likely very similar), the bulk of the fillers are basically quartz (silicon dioxide, it's in everything), a bit of corn starch, and a bit of lactose (which is a form of sugar). The corn starch and lactose isn't the best thing ever for your teeth, but it isn't like popping a sugar cube into your mouth either.
Of course brushing your teeth after the fact would be the ideal situation, but doing this on occasion isn't going to rot your face off either.