The Verbraucherschutz sued over this, and, apparently, BahnCard is not covered by this regulations as it is a (paid) Bonus programme, not a service or product in itself.
Is there a binding precedent (like a BGH or OLG ruling), or is that just someone’s theory that it’s not covered? I did not check. If there is no binding ruling, your Amtsgericht judge may see things differently. Even if the law didn’t cover it directly, I’d wonder about the spirit of the law. If contracts are covered where an actual service is rendered, shouldn’t that apply all the more to mere bonus programmes? I see no justification in treating these differently. Again, no research done - just a prima facie smell test.
At least that's what I got from the summary here:
https://www.test.de/Deutsche-Bahn-Kunden-koennen-Bahncard-la...