To begin with, I wouldn't be surprised if this is fueled by fringe right wing interests, similar to GamerGate etc. Second, I am generally in favor of CoCs and changes that aim to elevate minority groups. Thirdly, it's often hard to take "we have no problems with diversity" at face value when it comes from those favored by a lack of CoCs.
All that said - This, to me, seems like a hard call to make. An updated CoC seems great, and I agree wholeheartedly with the spirit of it, and the need for it. On the other hand, I find the lack of definition and process it entails problematic. Hopefully it's a "two steps forward, one step back" situation and not the other way around.