You might find some M-Dot sites to be unstable on Google Desktop Search says Google

We reported a few months back that Google is starting to push every website for mobile-first indexing. This is because Google has been seeing a lot of demand in the mobile search results on its platform. Therefore, it is obvious that you would want to have a mobile version of your website inside Google Search. But it has been seen that websites don’t bother to create websites mobile-friendly. Instead, there are two separate versions of the same website with one of them being optimized for mobile. Google clearly doesn’t want you to do that and wants the same website to be seen on mobile as well as desktop.

For this reason, Google has started to do mobile-first indexing for every website that you add from now on. However, there have been complaints that sites that are marked with M-Dot behave differently on Google Desktop Search. Now, Google’s John Mueller has addressed this issue in a Q&A session. “So from our point of view with an MDOT site with mobile-first indexing it’s more likely that you would see the MDOT version in the desktop search results.” He added, “So it’s something where we would expect that potentially if you have an MDOT site this will kind of remain in a kind of an unstable situation like this.”

He also mentioned that “Again what I would just do there is make sure that you redirect from the MDOT version to the desktop version for desktop users. That also helps us to understand that connection better and to show the right URL at the right time. So that’s kind of the best way to handle it or rather be the easiest way to handle it. Of course, the best way to handle it would be to use a responsive site.”