I swear I did nothing, and suddenly it works again. I can go on duty. My problem was that whenever I tried to go on duty, lspdfr instantly crashed. I have a clean installation and no other plugins. It crashed every single time.
I thought I'll create a fresh crashlog, so I started the game and went on duty... I expected it to crash, so I can have the logfile. But it didn't! Now it works again for some strange reason. I didn't do anything!
Now I reinstalled all my plugins (tested them one by one), and guess what - they all work. I noticed that lspdfr crashes when I have installed Smart Radio. I don't use it anyway, so it does not bother me. I "accidently" installed it, because I use to have it in the past. Now I use Grab The Ped instead.
However, Smart Radio is ONE thing that seems to cause lspdfr to crash when you try to go on duty. So if you have it, try to delete it and see if it works for you.
Allthough, I wonder how long it stays stable for me this time...