Google wants the AMP version of your page to be equivalent to the main mobile version of that page. So if your page has a comments area, Google would like to see those comments in the AMP version as well. But technically, John Mueller said, Google would not consider the lacking of comments on AMP as a "content mismatch" error. At least not today.
John Mueller said on Twitter first that "Users want the amp pages to be equivalent to the normal pages, so if the comments are an important part of your pages, I'd make sure they're also on the amp version." But then added "Afaik we don't flag this as content mismatch at the moment, but if recommend making sure the pages are as equivalent as possible."
Here are those tweets:
Users want the amp pages to be equivalent to the normal pages, so if the comments are an important part of your pages, I'd make sure they're also on the amp version.
— 🍌 John 🍌 (@JohnMu) February 4, 2020
Afaik we don't flag this as content mismatch at the moment, but if recommend making sure the pages are as equivalent as possible. https://t.co/fFONwERwKX has the common errors we flag.
— 🍌 John 🍌 (@JohnMu) February 4, 2020
This site, this page, we do not show the comments on the AMP version. I do show it on the desktop, mobile and mobile-app version, but not on AMP. Why? Well, when we first launched the AMP version, Disqus didn't have a way to do that. They do now, but I just never added it. I should, probably? But I do have a link to read the comments in the AMP version, that takes you out of AMP and into the mobile version.
So far, I had no issues with content mismatch issues by not having comments.
Forum discussion at Twitter.