I just read the German (extended) section regarding taking private photos.
Very strict regulations IMHO.

It is possible - but ...

Excerpt from the mentioned Bavarian Palace Department website:

"Small quantities of photos for private use (only with the usual hand-held cameras for private use and without light and tripod etc.) does not require a permit, and is allowed unless this conflicts with conservation or organizational requirements or trademark rights. Use of any private photo material for further purposes is expressly prohibited. However, we regret that in the palaces with continuous guided tours, photography for private purposes cannot usually be permitted for organizational reasons."