I already know this game's probably not for me, but I can give you some (hopefully articulate) answers that may help you refine your focus and disclaimers.
3. Player decides he doesn't want the MC to fuck the sexy lady so he chooses the option I provide to turn her down.
4. Since the MC isn't going to fuck the girl she goes off and finds someone else who will.
Is that NTR?
No, since the player turned down the LI. However, since she's off fucking someone else, most people will not ever want to see her in the game again afterwards... And virtually no one who dislikes NTR will want to see her fucking the other person, or have her talk about having fucked or being about to fuck the other person.
If instead of a stranger at the bar the scenario involves someone the MC knows already does it become NTR?
Still no, but if that happens, most people who dislike NTR won't want to see her OR the person she went off to fuck ever again, and they still won't want to see the scene.
If I have a character in a pre-existing relationship before they meet the MC does that qualify?
Depends on the context of the relationship. If both members of the relationship become the MC's girls, then no. If the girl breaks off the relationship to be with the MC, then no. If the girl keeps fucking the person while forming a relationship with the MC, and the girl's partner is not in a relationship with the MC, then yes, it is absolutely NTR no matter the genders involved.
What if the MC is introduced to a character but before he has the opportunity to pursue her, she starts dating/fucking one of the other ladies?
Yes, this is NTR, since it is someone who is not in a relationship with the MC fucking the MC's girl.
Is the expectation that all characters in the game are completely asexual unless the MC is directly involved?
The expectation is that the player has zero need whatsoever to see or read about sex scenes that do not involve the MC. Period. They never help, and they almost always hurt.
Occasionally, two members of the MC's harem who are already in relationships with the MC having sex together can be okay without being considered NTR by most sane people (note that some extremists will still consider it NTR), but it's all about context. If they start talking during the scene about how much better the sex is than when they're with the MC, then yes, that's NTR.
It's all about focus. The narrative focus of a harem game (and the vast majority of lewd scenes) should
ALWAYS be on the MC and his harem. Any scene that is not featuring the MC and his harem needs a solid narrative purpose that helps further the story of the MC and his harem.
Scenes involving characters without the MC present are not going to be a huge part of the game. There will be some cutaways. You'll see the two crazy girls playing with each other a few more times. Scenes like that are just a way for me to give the player a little more info/foreshadow future plot points. I figured they'd be a lot less boring if there are some boobs to look at instead of just having the characters stare at the camera and narrate their backstory and motivations.
This is a common refrain I've heard, but it entirely misses the point of these games for the people who play them. Most people who play harem games are immersing themselves in the MC, so scenes that involve people who are not the MC are pointless at best, and off-putting at worst, no matter how sexy the girls might be. In general, foreshadowing scenes in harem games work best when they are
NOT lewd.
If the consensus is that this type of content counts as NTR then I'll add the tag. But I don't think the content would satisfy people who are looking for an NTR game so I'm trying to judge things from a middle ground perspective.
The middle ground
NEVER works. You're exactly right that this type of content will not satisfy someone looking for NTR, but it will also be aggressively off-putting for people who hate NTR. I usually refer to this kind of content as "NTR-adjacent", since the people who dislike one will almost always dislike the other, and vice versa.
Hopefully that helps you get a bit more of an insight into some of the complaints you're receiving.
Edited to add one more note: It is almost invariably better to pick one direction and stay in it: either a harem with the MC being the only person shown with lewd scenes beyond the occasional harem members messing with each other (which you'll want to make avoidable for those afore-mentioned extremists), or just go full-cuck and make it NTR, with dudes and futas stealing the MC's girls all over the place and the MC getting humiliated and never fucking anyone. There is functionally zero overlap between the fans of these two types of games, so never go for the middle ground.
Another note: many harem fans also dislike futas being the penetrative partners in
ANY scenes at all, so best to make those avoidable, too, if that's the player group you're aiming for.