Google's John Mueller stated the obvious, that you cannot opt out of the new mobile-first indexing process. John said on Twitter "Nope. The world has gone mobile already, we're just catching up" when asked about if there was an opt out.
Nope. The world has gone mobile already, we're just catching up.
— 🍌 John 🍌 (@JohnMu) November 6, 2018
What John is saying is that this is the future of how Google is going to be indexing web sites. This is how people are and will consume the web - over mobile. Thus Google does not want to continue to support both methods of indexing in the long run.
Make sure your site is ready for mobile-first indexing, if you have not yet been switched over yet. Ready or not, here it comes.
Forum discussion at Twitter.