Thank you FranckRookie for the hint.
I wrote a PowerCLI script that set the DRS Automation Level to manual before the VM backup starts and a second one that sets it back to fully automated after the backup has finished.
This is a workaround until we redesign our backup.
@pelanchelian: to disable DRS is not an option because I think that would delete all resource pools, there settings, DRS Rules and all DRS settings :smileywink: