Theories are fine. I enjoy making them, even. I just got burned recently by a different fanbase blowing up after their big dumb fan theory didn't come true, and I'm still seeing the fallout three months later lol. Like I said before, if anyone starts talking about secret weddings I'm leaving.
Okay I'm gonna go back to the Yuffie thing now.
Before I get started, I'm gonna put it plainly that, within the context of the original game, Yuffie having some big adventure in Midgar was not a thought in anyone's mind. That's not a thing that happened. I understand that, okay?
Now then; when asked why Yuffie was chosen as the protagonist of this DLC over someone like Cid or Vincent, Nomura notably stated that it was becauses the remake is "following the plot of the original" and as such, Vincent would be asleep and Cid would still be on Shinra's side. Yuffie was comparatively free to do whatever they wanted within this timeframe. This implies pretty strongly that he doesn't view the events of the DLC as coming into conflict with the original narrative, it's something that could plausibly have happened (your milage may vary.)
So let's examine that. What is Yuffie doing? She's on a secret mission to steal materia from Shinra, for the "new wutai government." Obviously a lot of the details about Wutai itself are different now, Godo is in jail, but I think that's neither here nor there in regards to this. This sort of mission seems right up Yuffie's alley, it doesn't seem like the machinations of outside forces that put her here like the plot divergences of the main story, which Sephiroth is very clearly involved with. This is just a thing she's doing because she's doing it, if that makes sense. If no time bullshit was happening, she'd still be in Midgar doing this, and since this is a period of time we didn't see her originally, it doesn't contradict anything outright anyway. At least until she meets Nero, which is where things get iffy since it seemingly contradicts DoC.
Things to take issue with: Yuffie hears the name "Deepground," and Yuffie's friend is killed by Nero, who in DoC she has no big reaction to meeting (though she does get oddly emotional at Shelke for having such a disregard for her older sister, which kinda reminds me of Sonon now...)
Like I said before, Yuffie could easily forget the name deepground, as she hears it once and never gets context for what it even is anyway, so I'd consider that not a huge deal. We never see her initial reaction to them in DoC, so she could have been like "oh shit it's those guys." It's harder to grapple with her reaction to Nero (obviously when DoC was written, Sonon was not a thing,) so I'm gonna hide behind what I'm still considering the smoking gun of the argument here, the whispers.
Outside of preventing Yuffie from entering the bar, the Whispers never get involved in this story. You can come up with plenty of nice little reasons for that, like "they're only concerned about Yuffie not meeting the main party," or "they have limited resources and are focused only on the main party" (they cover the whole city at one point but okay), "they're dead already from a 4th dimensional perspective," etc. But I feel like that's all just side stepping the real point. It is a huge narrative point that these force of nature plot ghosts exist solely to stop things that shouldn't be happening from happening, arguably the main plot of remake part 1, and yet they don't get involved with Yuffie whatsoever. Say what you will about Square's writing tendencies, but I think the simplest explanation is the correct one here: Square does not view the events of this DLC as contradictory to the original events of the game. There's nothing else too it, even if that seems wrong to you.