Can I ask you to please clarify where you stand on this? As per the above 3 quotes, I'm having a hard time lining it all up.
I feel that it is my job as a DM to provide an entertaining play experience. I feel the DM has the most control over the gaming experience due to his role in the cooperative fiction in a role-playing game. Players have little to no control over each other. They can't change their tastes, personalities, or other such things to suit another player at the table. It's too much to ask and I feel some DMs in this discussion are basically saying, "Everyone needs to get along and talk to the other person before making their character to be sure they aren't making something the other person would be unhappy with." I don't feel players should have to do that. They can do it if they want to, but I do not expect it. The player is only responsible for making a character that will be fun for him to play, not a character that will be fun for him and fun for player x,y, and z. He doesn't need to run it by the other players before making what he's making. Maybe I'm misunderstanding all of you, but it seems like you're saying Player 1 has to check his concept with Player 2, 3, and 4. I don't agree with that if that is what is being said.
My group usually does ask each other what they're making because they don't want to overlap concepts or have too many of the same class. Backgrounds are usually individualized. They don't check feat choices by each other unless they're min-maxing as a group like the bard who may take the Inspiring Leader feat to empower the Druid's pixies from
conjure woodland beings. That is coordinated group min-maxing. That is example of the players working together to enhance the fun of at least two of them, though it might piss off the other players. I guess we will see.
My main point of contention is fun is too subjective. I can't be sure one player will have fun playing with another character. The people usually get along, but sometimes they don't love the other guy's character concept or his play-style. I can't control that. I can only provide them with clear parameters as a DM that I feel will ensure some semblance of balance and mitigate some of the worse min-maxing possibilities.
I have more ability as a DM to control the fun of the group by making the adventure fun and ensuring each player gets spotlight time.
I've had optimizers and non-optimizers in my games at the same time before. To be honest, it's never been a problem to the point that I've felt the need to take action over it. With that in mind, I sort of feel this is an extreme scenario and falls a bit outside the scope of normal, but here's what I would do regardless.
If Player 1 is min-maxing to the point of breaking my ability to provide fair encounters for the rest of the group or something similarly disruptive, I'd ask Player 1 to tune his character down. I've done this in a game before, truth be told. Note however that the decision to do this is irrelevant to Player 2's concerns.
If the above is not the case, yet Player 1 or Player 2 are complaining to me about the other, I would have a conversation with the two of them and make it clear that they need to work it out. If their respective playstyles aren't impacting how I run the game, then it's a conflict between the two of them. As adults, I expect them to sort it out. The only reason I would step in to even say that is if one or both of the players came to me with complaints about the other one.
In other (brutal) words, I may be responsible to bring the fun as the GM, but I am not a babysitter or crutch to dodge social confrontation. Grown ups should be able to figure something like that out.
It's a common case in my group. They snipe at each other now and again. One saying the other min-maxes all the time and damages the game. The other guy telling him mind his business, he likes to build his character the way he wants.
I don't have any problem running either character. I make it as fun as possible for both of them as a DM. I've been DMing long enough to realize most of the fun comes from me running the adventure well. I leave them to work out their differences as they see fit. As you said, they're adults and can work things out amongst themselves. As long as I've given their clear play parameters, I let them have free reign to make their characters according to what will be fun for the individual player.