When I'm getting thoroughly wound-up with the politics of public-sector projects, I bear in mind that my external work makes money, runs smoothly and follows similar principles to the main job.
As a PM, I'm used to criticism. I've had people telling me "You're rubbish" when they really mean "I'm threatened by your thorough analysis and understanding of the problem". What I know now is that I can successfully run my own business that they aren't involved in the politics of and don't influence. It works great for me in the wider world, so what's different here that makes our projects a nightmare and prone to failure? Oh yeah...it's them.
I also understand much more about the financial side of business and how little things like setting out the deliverables, cashflow, payments, reconciliation, and completing the work that the customer asked for impact the business in a big way.
My business also gives me a calm clarity. If the main job sacked me or made me redundant, I'd be able to scale up the external business in a few days. So that allows me to make decisions without being scared about what people in the organisation can do to me. I can force best practice, recommend the best solutions and call people out on their politics because the worst thing that can happen is it'll end the thing that I believe passionately in but also gives me the most grief!