I haven't found a single site for personal finance management that does bank syncing in Germany. Some that for example do Barclays, restrict to US or UK accounts.
Is there any law in Germany disallowing this?
I don't think there is a law against it. For example comdirect offers multi banking so you can access your accounts from other banks through the comdirect website.
My guess would be: Germans are very conservative when it comes to their money (preferring cash above cards, using "safe" low interest saving accounts instead of stocks) so there just might be no market for such a tool.
As much as I know StarMoney has also a web service for banking.