How to evangelize DevOps and tools in a low acceptance environment?
This is not docker-specific, but this general rule for evangelism applies: different audiences require different evidence.  In general, software developers (and managers from a development background) want to see it in action, so POC's with measurable outcomes are preferred.  Other disciplines and executive stakeholders may be OK with case studies and presentations before giving the greenlight; your goal is to identify which audience you're talking to, and begin to build a comprehensive argument.  

Start small; find one key stakeholder, and present your case using the evidence that best suits them.  Be patient; change in mature organizations is usually slow, so getting a small project up and running is a major accomplishment.