A mobile friendly website is a prerequisite to great search engine visibility. It’s easy to understand why since way back in 2014 over 60% of American Adults owned a smartphone. [Pew Research: mobile tech fact sheet] Today, with that number likely a little(or a lot) larger and with the overwhelming “wireless” marketing assault on our senses, it’s only logical to have a mobile friendly site.
I have first hand experience since many of the sites I manage were around before smartphones. And many other sites I’ve SEO’d did not pass the Google mobile friendly test at first. It’s a fact, being non-responsive hurts a website’s usability so it makes sense that search engine rankings would falter.
It’s not difficult to get your site responsive and if you use WordPress with a modern theme it probably already is. But if you keep getting annoying emails from Google Webmaster tools informing you of mobile issues definitely take notice.