This is highly country specific. For the marriage record, I checked the laws in Germany, and (except for your own records) you have to present a "legal interest", which seems to be stricter than a "legitimate interest" (i.e. probably you need the information to enforce your rights, not just because you want to do genealogy). I'm pretty sure the others would count as particularly sensitive personal data too.
You can also not be on the role but you cant vote in that case.
When governments in the EU started digitizing their data like 20 years ago, it used to be that lots of personal data would end up published on official websites, either in the form of scanned PDFs that Google would gladly OCR and index, or in directly readable formats. Since then, the EU has cracked down on all of that, and you can no longer search for someone's phone number in order to get their full name, address, date of birth and ID. Even data that used to be available just 10 years ago, now has been removed.
(Ignoring that the GDPR doesn't even apply to governments)
I have similar assumptions, but what about the less technically inclined citizens?
Moreover, I wouldn't be surprised if the ploy described by the OP:
> Could I request this data myself, then start emailing them scam emails "I know you contacted us in June, could you call me on 555-1223 etc"
would work on me. Really, it would take me checking DKIM and/or SPF to notice such an email. And from this story it seems likely the city of Seattle doesn't actually implement DKIM or SPF.
That's because you're not corresponding with case officers and police officers.