I agree 100% with you that the NEA does nothing to help the reputation of teachers and in fact hurts it. I am not a member of the NEA, and hopefully never will be. My membership in the NEA may be forced upon me if VA turned into an 'at will' state, or if my husband and I move to another state before I retire from teaching. Virginia is a 'right to work' state and I cannot be forced into a union.
All that being said....IMO the public schools are largely a reflection of the community - and of the most liberal part of the community. That would explain why those posters in red counties and districts have fewer complaints about their schools and those in blue counties refuse to allow their kids to attend. My SIL's husband is a Lutheran minister in inner city LA and they live on the outskirts of the city. She never considered sending her kids to the public school system and I was relieved when she said she was going to home-school them. Her oldest now is a rising 9th grader and he will be attending a boarding school in Minnesota.
There is no 'one size fits all' answer. I completely support anyone's decision to home school or to use private or Christian schools or to use public schools. There are very few parents out there that are incapable of making a good choice. So when someone tells me that their public school is good/bad choice, I take them at their word and don't try to change their minds and force them to do what I say when I am not living their lives.