Any password makes it impossible to print this file in a professionel manner. If the printer has to print it he will always be able to edit it in several software products. If you don't trust the printer a password would not be a solution neither because there are ways to get rid of it.
A raster image as Sandee mentioned, would redouce the quality of the output. Text and vector forms would become blury and not crsipy and clear any more and it might happen that the file size is increaing (depending on the content).
If I would have an issue with the printer I would choose another one. Maybe that there exists another printer in the country where you live, take the other one.
Are you worried that they are opening the PDF in Illustrator and might accidently edit or move/delete something?
All printers would have either Acrobat or Adobe Reader which is free, so there is no reason for them to open your PDFs in Illustrator.
Perhaps they are opening them in AI to correct problems in your PDFs. Ask them if there are any issues, it's possible your InDesign or PDF creation process is wrong for digital printing, (for example, Rich Black text that needs to be converted to 100 Black only, etc.)
Or maybe they are doing imposition.
However, opening PDFs in Illustrator is still not a good idea. Illustrator is NOT a general purpose PDF editor.
In Acrobat Pro there are Preflight Profiles and Fixups that may correct some issues.
PitStop Pro is a better choice for correcting issues in PDFs. And there are also third party Acrobat plug-ins for impostion purposes.
A RIP with software specifically designed for it will also help fix PDFs without resorting to Illustrator.
Since your printer is in-house, I suggest you have a meeting to ask if they are opening your PDFs in Illustrator and why they are doing so.
Perhaps some guidelines should be agreed upon by both sides and enforced by some rules.
I have a feeling that some additional training (possibly on both sides) is needed to straighten out this situation.