In registering for this site, I was told I could not register unless I enabled third-party cookies.
I'm still waiting for your reply on who exactly told you that, but it's not true. Actually, I just found the message; it's returned by our OpenId provider. This may need some updating, since it's really not true.
I can think of no good reason why a site should require third-party cookies and, therefore, I do not intend to allow their use in the general case.
There certainly are good reasons for third-party cookies to exist. They're a great feature in particular when you have a network of sites that spans several domains, and want to make the use of that network more convenient to users. That said, any tool can be abused, so I can comprehend why you're wary of allowing them.
As I said, we do not require them.
All features that a browser could consider third-party cookies (even though they actually aren't for the most part; see my answer here) are totally optional. They make some stuff nicer and easier for the user, but they're not required.
This includes using
localStorage access in a cross-domain IFRAME for the global login, so a user doesn't have to log in to each site seperately (but they're obviously free to take that extra step if they don't want to allow any cross-domain data), and the OpenId creation shortcut may require actual third-party cookies.
But since you're neither required to create an OpenId with us (you can use any other), nor, even if you want to create one with us, you're not required to do it right there (you can also go to StackExchange OpenId directly), disallowing cross-domain data does not prevent you from using the site.
Ironically, I have made a session exception so that I can ask this question.
Welcome to Stack Exchange :) You can clear all third party cookies now; the sites will still work.
Please can you tell me why third-party cookies are required for Stack Overflow, and specifically why they are so important to the site that they are a requirement for (new?) users.
Once again, they are not.