A recent side advert for a question on UX.SE (this question) appeared with the squared paper beta design background, is this because UX.SE is still in beta or does a site's design need to include these ads?
The ads are most likely computer-generated as they seem to be based on the hottest questions. The scripts probably take into account of the "beta-ness" of the site in question and render the beta design accordingly. And since UX.SE is in beta:
The ads for UX.SE ends up with the "sketchy beta" design as a result.
Although UX.SE seems to be the exception to this meta SO answer:
That is the "Sketchy" beta theme for all beta sites. When a site makes it out of beta, they will choose their own logo and design.