Good question Ruth, and one with an easy answer. If they have no appreciation for design and think their current website is fine, then they aren’t a client you want. If you did convince them to do a project, that same lack of appreciation and respect for design would carry through and probably create a very unsuccessful and unsatisfying result for everyone.
It might be worth a single effort to try to explain the value of good design and user experience to them (with concrete examples to back up your claim), but if they don’t catch on the change their tune right away, walk away. You’ll find something better. As Obi-won might say “this isn’t the client you’re looking for”.