Ashley Berman Hale, a personality very active in the Google Webmaster Help channels, posted on Google+ an email she received from a company with the subject line "Google Removing Your Site From Search Results This Month!"
It then goes on to read, "Did you know Google will demote or delist you from their search results if you don't have a mobile friendly site by April 21st?"
Liars! Google will not delist web sites for not being mobile-friendly. Google may demote the sites in the mobile search results if your site is not mobile-friendly, but delisting is a lie.
Google's Gary Illyes posted on Twitter a response:
So I don't mind getting people motivated to go mobile friendly, but I do mind spreading false things. Not nice, guys https://t.co/0X0VxMQlIE
— Gary Illyes (@methode) April 15, 2015
Google's John Mueller posted on Google+:
It's great to get people motivated to make their website mobile-friendly, but we're not going to be removing sites from search just because they're not mobile-friendly. You can test your pages & reach our documentation (including some simple tweaks that might work for your CMS too) at http://g.co/mobilefriendly
I hate when people lie to get business or lie for anything really.