Regarding meta-gaming being equivalent to cheating... consider a player who evaluates (from the perspective of their character) that the best chance of success comes from splitting the party. The player opts not to push for this course of action because splitting the party would make the game less fun for that particular group. Is it meta-gaming? Yes, by definition. Is it cheating? Absolutely not. Indeed, many consider it poor form to make IC decisions that detract from other players' fun. (Consider, e.g., stealing from the party with the justification that "it's what my character would do".) Ergo, meta-gaming is not equivalent to cheating.
Meta-gaming is definitionally not role-playing, and role-playing is the method by which a role-playing game is played. Using information that the character does not have - such as the fact that the characters exist as a game for people living in another dimension - is meta-gaming, and therefore bad.
Of course, making the other players sit on the sidelines while you go off on your solo adventure is also bad. In this case, you're put into the difficult situation of choosing between two bad choices: you either prevent the other players from participating for some significant period of time, or you damage the integrity of the entire exercise and everything that's happened so far by choosing to act out-of-character. Weighing the (likely) significant inconvenience you would pose to the group, against the (likely) minor damage to suspension of disbelief, you may well choose that meta-gaming here is the lesser of two evils. That doesn't make it a
good thing, by any stretch; it's merely
less terrible than the alternative at the time. Ideally, players should not make characters that would be prone to such dilemmas, since there is a cost to be paid either way.
Second, out-of-character decisions, by definition, can't qualify as meta-gaming. Tailoring the campaign to the party usually involves the DM making out-of-character decisions about the content of the game world. Yes, those OOC decisions should be made with an eye towards consistency with the IC events of the campaign thus far, but that still leaves a huge range of possibilities for the DM to select from. Selecting those options suited for a particular party cannot be meta-gaming, by definition, because it wasn't an in-character choice to begin with.
The DM is responsible for role-playing all NPCs in the game. That includes the NPC who designed any given trap, and decided where to place it; even if that character died a thousand years before the campaign began. If the DM is using their out-of-game knowledge of who the PCs are (or their absolute bonus with thieves' tools), to make decisions for this NPC who never met the party, then that's meta-gaming. Likewise, if there are eight kobolds in the next room instead of four, if their decision to congregate was based on information they could not have, then that is meta-gaming.
My answer to your question regarding the fighter and roleplaying is similar. To the extent that character-building choices reflect IC decisions, the character doesn't know what is mechanically optimal because the character is unaware of the game mechanics. The choice whether or not to optimize is therefore largely an OOC choice. Sure, there is an IC component too, regarding how the character wants to spend their time. But I don't accept that the only IC choice that qualifies as "good roleplaying" is "to be the best fighter they can be". Characters, like people, are multi-faceted, and it's not bad roleplaying to play them that way. Would you really argue that a fighter who spends one of his ASIs to take the Gourmand feat, for example, is roleplaying poorly because IC they spent time to learn how to cook rather than spending that time to be the best fighter they can be?
Of course the characters don't know the game mechanics. They don't need to, because they can observe their
actual reality, of which those mechanics are merely a reflection.
They understand the costs associated with making one choice over another, far better than we do.
A fighter may well choose to become a Gourmand rather than a Great Weapon Master. There are plenty of reasons to make one choice or the other. However, it is disingenuous to remove the
pressure to optimize, which was the suggestion at hand; whether the fighter chooses one path or another, the knowledge that this choice may have ramifications is not something that should be ignored. If the
player knows that the future opposition will
causally re-balance itself to account for the capability of the character, then that is meta-game information which the
character is not allowed to consider when making their decision.
Third, I stridently disagree that DMs always need to avoid meta-gaming. At some tables, such as yours, they absolutey do need to avoid metagaming, because DM metagaming would clearly detract from the fun of the players at your table, and detracting from the fun of the players is a bad thing. But at tables like mine where metagaming is an expected (and explicitly acknowledged) tool in the DMs toolkit, DM metagaming can instead enhance the fun of the players, and therefore can be a good thing. (Like all such DM tools, care should be taken not to rely on metagaming too heavily, lest it lose effectiveness.)
If you find that role-playing is detracting from the fun of your role-playing games, then you may need to find a new hobby. If you want to meta-game then fine, but you aren't role-playing anymore, and to suggest that you are would be a lie. It may sound harsh, but it is already true whether or not you acknowledge it, and owning up to it doesn't make it any worse.
Finally, I'd like to point out that your post came across as a personal attack on my integrity, and as an accusation that my prior post "damag[ed] the integrity of the role-playing community". We merely have different playstyles, and while I am happy to discuss the differences with you, and recognize that you don't like my playstyle, I would ask that you refrain from insinuating that my playstyle is inferior (let alone that my choice to discuss my style publicly is damaging to the community itself).
Misrepresenting the role-playing hobby, by suggesting that meta-gaming is a valid playstyle, is not something which should ever be tolerated. Meta-gaming is bad, in the context of role-playing games, and meta-gamers are bad role-players definitionally; they are role-playing incorrectly, if they can be said to still be role-playing at all. If you take offense at that, then you may need to re-evaluate your perspective. That which can be destroyed by the truth should be.