Well, I"m of the opposite opinion. I don't have a sweet tooth at all, and I dislike sweetened ciders and wines and even hard lemonade!
The rubber stopper taste and smell is not related to tannins- I actually add tannin to my apple wines to provide "bite" to them. I would think there were be no (Or at least very little tannic taste with apfelwein).
That taste/smell will fade, and you won't even notice it after a while.
That said, if you want to sweeten it because it's too dry, you can sweeten a sample to taste. And then add a proportional amount to the rest of the batch. Keep in mind that a month after bottling, it'll taste even sweeter. So, sweeten it just a tad to under where it's "just right".
Broken Leg Brewery
Giving beer a leg to stand on since 2006