@Marius Leitzgen, Thanks for posting in Q&A.
Currently, there is no such related policies in Intune that can block OneDrive starting.
For the error message, the troubleshoot steps in this thread are helpful based on my research.
https://www.reddit.com/r/Intune/comments/mzgl75/this_app_has_been_blocked_by_your_system/
Non-official, just for reference.
After that, you can try to uninstall OneDrive and re-install it to see if you can start it. By the way, could you please share with us what kind of program you cannot start? Did you cannot start OneDrive program, or you cannot start OneDrive sync or something else you cannot start?
Please try above information, if there is any update, feel free to let us know.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.