I have built a project with Polymer 1.x and played with Polymer 2. It is production ready and I have seen websites built with Polymer. In my own point of view Polymer is not "developer-friendly" as it has it's own "syntax" which has gone a little bit too far from native code. The second issue is that Polymer 1.x (and 2.x) have performance issues and thus they're may be a problem for mobile or "weak" devices (i.e. tablet-pc/netbook).
I advise you to compare web-component libraries (webcomponents.org/introduction) and compare performance (rawgit.com/krausest/js-framework-benchmark/1922d6… - scroll down to non-keyed implementations).
Summary - Polymer is production ready. But it's not the only one.