If you are redoing your website and your developer is offering a non-mobile friendly option, please read these statistics before making your decision: http://karenmcgrane.com/2013/06/13/state-of-the-mobile-web-sources/
Your new website should be around for at least the next five years – possibly much longer. We view websites on everything from TVs, tablets, desktops, laptops and mobile phones today. Technology advances very quickly and new devices come on the market daily. The best approach is to not target one device, but allow your website to reflow content and shrink images so the site fits well on any device of any size.