You have put a lot of stuff into your question and I have broken it into a number of more concise questions:
1. Is it appropriate for a GM to critique "poor play"?
The GM in a RPG serves a number of functions: a) creator and player of the world b) impartial referee and c) coach, particularly to new players or new to the GM. If the player's and GM want a debrief following a session or adventure can be mutually beneficial: for the players it can show where they missed clues or options that would have made things easier and for the GM it can show areas where he a) failed to communicate enough or, more rarely, too much information, b) over or under-estimated the player and/or character capability and c) used ideas and techniques which were or were not fun for the players.
2. Does "poor play" include poor understanding of or reaction to GM or campaign style?
In general, No.
I refer to my answer to My PCs have a plan that will get them all killed; how and why should I save them? where I discuss player agenecy. In summary, agency is:
Players making informed decisions that have reasonable consequences.
The information resides with the GM, it is their job to ensure that the players have it. How explicit that is depends on the style of the GM taking into account the skill of the players and always remembering that things that look crystal clear from your side of the screen may be opaque from the player's side.
3. Is it appropriate for a player to critique the GM's story or characterisation of NPCs?
But such criticism should always be in the form of "I didn't like ..." or "I would have preferred it if ...". This is part of the two way communication that allows the GM to make sure they produce stuff both they and the players want to play.
4. Is it appropriate for a player to demand more "motivation" (intrinsic or extrinsic) for their character?
In character, Yes.
In a situation where a mission or adventure is being pitched to the character, they have three options a) "No", b) "Yes" or c) "Only if ...". Which means, a) they ignore the hook, b) off we go! or c) an NPC needs to negotiate a fair reward (remembering that negotiations can fail). A GM interested in agency should not (or at most rarely) force the characters into situations where they feel the reward is not worth the risk. If that means they pass on your pet adventure then so be it; maybe they will come back to it, maybe you can use it in another campaign.
If the player didn't feel the character would be appropriately rewarded; why did he take it on the adventure rather than letting it spend the night in the pub?
5. Is it appropriate for a person to use their character as a mouthpiece in the real world?
No, this is My Guy Syndrome and your analogy with "I'm not a racist, but ..." is very apt.
6. For all of the above, how do I deal with interactions that I find condescending, dismissive and rude and show little sympathy for alternative points of view?
You deal with those types of interactions as you would any in the real world; appropriately.
First of all, recognise that you are responsible to your reaction to what they say, not them. Your emotions are yours, not theirs.
Second, admit the possibility that they may not intend to cause offence. Some people, for whatever reason, are more assertive of their opinions and less accepting of alternative views than other people. This is why we have partisan politics :).
Third, employ strategies to deal with it.
There is a story which has been often quoted (I cannot find an original source ) that when Field-Marshal Montgomery was robustly (“They’re balls, sheer balls, rubbish!”) criticising General Eisenhower's strategy, Eisenhower reached across, touched Montgomery on the knee and said: “Steady, Monty! You can’t speak to me like that. I’m your boss.”
Weather it is true or not, it is a perfect example of how to deal with criticism that has descended into abuse. Even if you don't have the authority of being Supreme Commander Allied Expeditionary Force, you always have the right to politely state that you find what the other person is saying to be offensive and that your offence arises from how they are saying it not what they are saying.
Once the circuit of abuse has been broken, you can guide them towards more non-confrontational language. For example, you can ask that they phrase their statements as "I would ..." not "You should ..." which implicitly allows for different opinions.
If the persist in abuse then naturally, as politely as you can, be very, very rude!