It is asking a lot to ask people to make ultra fine judgements on contamination. The takeaway for me is if you can see it(contamination), toss it rather than recycle. So cheese(and oil) encrusted pizza boxes would go in the trash. 

Yes, there is a lot of hypocrisy and self-righteousness floating around and a lot of denial. If we as a society truly cared about the environment there wouldn’t be a need for recycling at all( certainly a lot less than there is). The environment always takes second place to profit and convenience. Just employing the term "pro-environment" shows how divorced from reality we are. 

I hope all that thorough washing you do is with reclaimed water. Personally, I just put mine through the used dishwater and call it good.