In the same vein as fostering innovation and accountability at a grass-roots level, you need to work across the wider organization to ensure they accept the fact that change is a good thing and not something to be feared.
It is true to say that changing anything on the production platform—be it a new piece of technology, a bug fix to a 15-year old code base, an upgrade to an operating system, or a replacement storage array—can increase the risk of the platform, or parts thereof, failing. The only way to truly eliminate this risk is to change nothing, or simply switch everything off and lock it away, which is neither practical nor realistic. What is needed is a way to manage, reduce, and accept the risk.
Implementing CD and DevOps will do just that. You have small incremental changes, transparency of what's going on, the team...