First I tried the option "Preserve these tags from being cleared or overwritten with MusicBrainz data:" in the Tags option. This was suggested in some entries I found with an Google search. This does not prevent Picard from writing the AcoustID in mp3-files.
Then I extended the no_release.py-plugin to get rid of the acoustid_id and some other unwanted tags. It does remove all unwanted tags just fine - except the acoustid_id.
OK, next try: I extended the file renaming with $unset(acoustid_id) and also tried $unset(%acoustid_id%). It doesn't help, the AcoustID-tag will still be written to the files.
At last I tried to do the same with the Advanced->Scripting option. No success, again.
I also have tried to toggle all the options on the Tags-options page.
It is not possible in any way, to get rid of the AcoustID, acoustid_id tag.
Any help would be appreciated.