I've not been brave enough to totally "check out", but I do avoid sensationalized news and try to pay more attention to valuable information rather than "drama".
Meanwhile at work I always remind my team "Hey we are not curing cancer, relax, slow is fast, fast is slow."
I tell my teams my job is easy because as a manager I only have four things to do:
1) Provide Air Cover (reduce stress)
2) Provide resources
3) Provide direction
4) Get the F* out of the way
I find that #1 is harder than it sounds, but as this article points out stress is infectious and can really slow a team down. I've had more than one stressed out employee come into my office and explain how we're missing some deadline or whatever and I always say "Yup, ok we'll get through it, we're not curing cancer here." we both laugh and they walk out with a lighter step to their walk.That said I believe in accountability and we try to pick these things up in retro's and figure out how to avoid them in the future.
I like to say "I like originality in mistakes, big massive mistakes are fine, just learn and try not to repeat them."