Criminal proceedings are usually public in most countries. Where do parking tickets fall? Even if not technically criminal, some might, for the same underlying reasons, consider it acceptable for "someone well-off whom you don't like and who doesn't seem to mind getting tickets on a regular basis" to have this illegal behavior on the public record. "Don't want your name tarnished? Don't park illegally."
[Edit: on the other hand, if the ticket is unfair (eg. confusing signage as in this example), then you have a valid point; I just wanted to point out the other side of the coin]
Don't know about where you are, but in Ontario Canada (the only place I've gotten in enough trouble to care about the difference ;-) ), there is a criminal code and the highway traffic act. There are illegal things that you can do in your car that may be in either or both areas.
"Criminal" means in the criminal code, but both are illegal. I think that you don't have a right to privacy for either because it obfuscates the application of the law. Indeed, the Japanese government can query the Ontario government to get a list of transgressions that you had while driving a car in Ontario (I know this because they did so when I converted my driver's license to a Japanese one -- and they didn't need my consent).
I think OP's use of the term "criminal" is a bit loose, but I would be surprised if you have any right to privacy for a a fine levied due to a legal infraction. Whether or not you should have a right to privacy is a completely different conversation...
Aside: It was important to me because many years ago I inadvertently drove while suspended. I had an unpaid ticket that I had forgotten about and my license was suspended. The suspension got lost in the mail (first a postal strike and then the delivery person put my mail in the wrong "super box" -- I eventually got it months later). When I was first getting my visa for Japan, I needed to find out if this was a criminal offence or a highway traffic act offence.
In WA at least all traffic offenses are public record. You can go search court databases by either name or license plate to get the full details of any tickets and charges in that system.
What you say is true. It's also the case that there's a lot of information that is nominally public--often for very defensible reasons--which historically took significant effort to get at and, even then, only in a very limited and manual way.
Today, a lot of that information is at least a lot more accessible to everyone (though in this case it still took a lot of work) and, furthermore, it can be mashed up with other public or semi-public data.
I'm pretty sure this is something we'll be collectively be coming to terms with for a long time.
Voter registration records being a perfect example - anyone can look up my address because the state makes it incredibly easy to pop my name into a website and there it is.
Of course, historically you could look up the address for most people through the white pages.
But that doesn't change the basic point. If you were to ask if you should be able to look up anyone's physical address by typing their name into a web page, I suspect many people would say no. Yet, here we are.
(I also suspect that many would be really shocked at the amount of info available about them from "deep web" searches much less via a $20 online background check.
[Edit: on the other hand, if the ticket is unfair (eg. confusing signage as in this example), then you have a valid point; I just wanted to point out the other side of the coin]