Hi Alfonso_S,
We understand you are having an issue with moving your pinned Safari tabs and we're happy to help. Does the issue occur after restarting the Mac using the steps here: Log out, sleep, wake, restart, or shut down your Mac ?
Does the same issue occur in safe mode? If you are not familiar with the safe mode steps, you can follow the steps here: How to use safe mode on your Mac to get it done. Once in safe mode, you'd want to use the Mac as you normally would to see if the issue occurs again. You can tell when the Mac is in safe mode because on the desktop it will show the words Safe Boot in the top right-hand corner of the screen.
Lastly, does the issue occur in a different user account? If you already have another user account set up, then you can use that one or create a new one to test in using the steps here: Set up users, guests, and groups on Mac
Take care