Going non-responsive (and building two parallel sites) is ok too - think about it- do you like most mobile websites that you visit?
Don’t get me wrong- there are many practical reasons for having a responsive mobile website, and many of the sites I’ve built over the past couple of years are responsive. But, just because we can do something with design doesn’t mean we should or that it’s a better experience. There are times when a site built for a mobile device is better then building a responsive site.
I try to take in the user’s perspective when deciding whether or not to build one responsive site or two parallel sites. In many situations, the needs of someone visiting a site while on a phone is not going to be the same as when they’re sitting at their desk or on their couch with a laptop.
As an example, I have a client that delivers medical services. Patients and doctors visiting the site from their desktops are expecting a much different experience than those visiting on their phones (researching procedures, downloading forms to complete at home, reading doctor’s CVs, doctors logging into the physician portal vs. people wanting to know the hours, directions, phone numbers, etc.). As a result, we made the decision to create two parallel sites (one for desktops & tablets and one for mobile devices).
I use Mobilize to divert folks to the correct page (each page of each site has customized header code so that they are alway directed to the corresponding page of the correct site…and not just to the homepage). I also deploy annotations in html and the sitemaps that let Google know about the corresponding sites/pages. And, unless something has changed, Google is perfectly fine with two parallel sites - so long as these annotations are used correctly (see: https://developers.google.com/webmasters/mobile-sites/mobile-seo/separate-urls#tldr ).
If you’d like to compare one of my pages versus a different company that’s in the same field, you can do so at the following address (be sure to pull it up on a mobile device!). Now, pull up virtually any hospital or free-standing medical imaging site, and I’ll bet you’ll find that it’s a) responsive, and; b) not nearly as easy to find what you’re looking for.