The discussion of this complex and important topic is long overdue, but I am a bit disappointed to see it veer off in so many directions, despite Sisiutils best attempts to keep it on track.
1. Framing the discussion
Ethical play = fair play
To help clarify, I believe it was the OPs intention to get to a definition of ethical playing in the sense of what constitutes fair play. A game is fair if all players interpret and apply the rules in the same way, so coming to a consensus about which settings and ways of playing are in accordance with the rules should be the goal of the discussion. This goes for multiplayer as well as singleplayer, since we compare strategies and outcomes of our sp-games on this forum.
Personal ethics vs shared play ethics
If we accept this premise, the posts about whether people find the use of slavery, fascism, nuclear weapons etc. in accordance with their personal ethics, while interesting, are beside the point. The game rules include these choices and the fact that some people consider them to be in bad taste should have no bearing on the consensus of what constitutes fair play.
2. Hard limits: Fair = Comparable
Nonstandard games
Before we look at the application of certain rules, lets first exclude from further discussion what I would call non-standard games. These are games where the rules and assets (map-tiles, cities, buildings, units etc) are changed or added with a mod or the worldbuilder. While these games may well be played true to their particular rules once they start, the games themselves are different from and thus not comparable to the standard configuration of civ and should therefore be excluded from further discussion.
Picking opponents, maps and other settings
In contrast, any game that applies particular settings included in the original (and patched) versions of civ should be considered a standard game and discussed further. There has been some debate about whether picking extreme combinations of map-size, number and kinds of opponents, speeds and rule-variations to beat, say, deity isnt cheating. I would say it isnt, as the game allows for these configurations and the games can be compared fairly to games with the same settings.
When it comes to bragging rights though, all the settings used should be mentioned to allow a fair estimate of overall playing skill. I would argue that it requires more skill to win the game the more settings are randomised, but non-random setups are the same for all players and the games are thus comparable and fair.
Improving your chances
Another hard case for exlcusion from what constitutes comparable, fair play are actions that alter the odds of random decisions in the game. The most common case is reloading to replay turns with unfavorable outcomes, but it also includes restarting games to get a better starting location. While there is nothing ethically wrong with playing like this per se, it does mean you are cheating if you are comparing your games to those of others. The same is true for looking at the map in worldbuilder, which gives you information other players do not have.
Bugs
Lastly, we should consider all moves to be unfair that exploit faulty technical implementation of the rules or coding bugs that allow you to suspend the rules of the game, such as avoiding army support cost by staying in permanent anarchy or repeatedly trading the same map to the same AI for gold. A good indicator for such bugs is that, in gameplay terms, they give you something for nothing. Although these moves are made possible by the game, they allow you to situatively void its rules and should thus not be used.
3. Soft limits: Exploits
With the preceeding paragraphs, we have eliminated setups and ways of playing that are reasonably clearly outside a body of rules that allows for comparison and thus fair play. More problematic are exploits; ways of playing that are allowed for by the rules but give the player an advantage that upset game balance and implicitly create dominant choices, reward micromanagement or systematically take advantage of AI behaviour.
Dominant Choices
Good examples for this can be found among game mechanics from previous versions of civ that have been changed; i.e. the power of certain units and traits, or tactics like early chopping. The goal in altering these mechanics was to allow for a more balanced and varied playing experience.
We play games to improve, test and compare our skills: If one choice in the game (i.e. playing a financial civ or building a worker first and chopping all the forests available) is dominant meaning clearly and consistently more advantageous than others - little skill is required on behalf of the player, the number of useful choices is diminished and the game as a whole suffers.
The problem lies in finding these mechanics (they often take a long time of playing before they become apparent) and determining whether they affect game balance to a degree where they need to be changed which is where the discussion becomes interesting. I cant think of any game mechanic that is clearly broken to the point that to use it would be unfair, but I have a few candidates where I have my suspicions.
One such example is slavery/whipping, especially under vanilla civ 1.61. True, this feature is in the game to let you convert people (food) into shields, but I suspect that the happiness penalty for this is inadequate, especially if you are sacrificing two or more pop-points in one go and use the spillover on projects that cannot normally be rushed. Combined with theatres and the culture slider, pop-rushing gets you large gains for very little cost. Although poprushing is clearly a dominant tactic compared to just building, I still consider it fair to use at the moment but I would like to see it nerfed.
Micromanagement
Another problematic category is anything to do with micromanagement. Examples of this are using pre-build of units to save on maintenance cost, switching production mid-turn to take advantage of chops, using binary science (100 or 0%) to optimise research yields on commerce and pre-chopping of forest to reduce build times for a wonder. While neither of these techniques are in violation of the rules, they do reward a way of playing that, for most players, is detrimental to their enjoyment of the game. Again, I would not consider it unfair to use these techniques, but I would like to see them made ineffective in subsequent patches.
AI-Exploits
The last and probably most controversial category of exploits take advantage of how the AI is programmed. Common to all of them is that the player acts with foreknowledge of what the AI will do (based on experience) and uses tactics against it that would not work against a human player.
Of course, in the broadest sense, a game against the AI is always intrinsically unfair: The AI gets boni (uses different rules and starting values) to compensate for its strategic and tactical inadequacies (waging war, pursuing and preventing certain victory types). But since every human player competes with the same inadequate AI, the games can still be considered fair in that they are comparable to each other.
Therefore, players who use AI personality (preferred civics, religious affilliation) to their diplomatic and military advantage, research tech that the AI doesnt prioritise for trade benefit (alphabet, drama or paper) or use military tactics that the AI does not counter well (bombardment, attacks from friendly AIs territory where you cannot be attacked back) are arguably playing fairly, because they build on a general weakness common to all games against the AI.
However, I would call plays unethical, or unfair that actively entice the AI to make a tactical decision to its immediate disadvantage. These include luring out city defenders with a worker and gifting the AI gold/turn only to reclaim in ressource trades that will bankrupt the AI once you withdraw the credit. The difference somehwat labored, but nonetheless is that the player does not take advantage of a latent AI weakness but actively tricks the AI for short-term gain. I am sure there are other plays against the AI that are debatable, but these two are foremost in my mind.
Summary
1. To be fair, games need to be comparable in terms of the rules used and adhered to. Games with different rules and in-game assets do not qualify for direct comparison.
2. For the purpose of a discussion of comparable games and playing skill, reloading and restarting, looking at the map in worldbuilder or taking advantage of technical faults in the code or the way the AI is programmed should be considered unfair (hard limits).
3. Use of unbalanced game mechanics and micromanagement can be considered fair play, but should be discouraged (soft limits).
It's one thing to not spread Judaism in the game because in real life, the religion is one of the few without a proselytizing credo; it's quite another to grind your ugly little prejudicial axe in public. 
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