With regular changes in the google search algorithm, now Google has come up with a new feature which will give freedom to have separate Google Mobile First Index for the mobile and desktop version of a website.
Google Mobile First Index

New Google Index news was announced by Gary Illyes who is working as webmaster trends analyst with Google, at Pubcon. The approximate date to introduced this feature in a live system will be the next month.
After implementing Mobile Index, the mobile-friendly website will have a different Index (sitemap) for the website. In simple words, the Index for the desktop version of the website will not be used for the Google mobile Index.
How to Optimize website for Google Mobile Index?
- Make Website mobile friendly, check website template in different screen variations. (This can be done in Google Chrome Developer Mode.)
- Use Google Mobile-Friendly Test for the website, you can use an old version of Mobile friendly test and for the new version try Google Mobile friendly test.
- Above test will help you to understand whether your website is 100% Mobile friendly or need any changes to achieve 100% mark.
- Regularly Check Mobile Usability option in Google webmaster tools, here you can know which page of your website needs changes for the friendly mobile version of a website.
- Check Your website speed for the mobile version using Google page speed tool.
- Use new technology called AMP (Accelerate Mobile Pages) that optimizes your web page, and speed up your page according to mobile search engine result.
If you want to know what is AMP technology in details then read my previous article: What is AMP page?
You can install AMP plugin for your WordPress website, for better result install two plugins as describe below.
- Install Accelerated Mobile Pages plugin by kaludi brothers.
- Install AMP plugin by Automattic.
Why there is need of installing two plugins for enabling Accelerated Mobile Pages in the website? Actually, plugin by kaludi brothers is used for customizing website pages according to AMP rules and the AMP plugin by Automattic will internally help to change it’s coding according to AMP.
Conclusion: I will suggest you change your website according to mobile version so that it can be in the race of Google mobile first index in future. We did ask Google for more details, but all it would confirm is the general timing of the change. Stay tuned for more in a few months, it seems.