Why wasn't the plate-drop the line the Turks could not cross, the order they found they couldn't bring themselves to carry out? It's an interesting question, by which I mean it's a question that helps to make them interesting characters. They've been doing bad stuff for so long that the difference between the platedrop and all the previous things they've done in the line of duty is merely quantitive, not qualitative.
It does make the characters interesting to me, though I'd argue it's also a qualitative difference in that many of their previous victims would have had motive for killing: terrorists, enemies of Shinra, etc. Whereas the casualties here were the people - including innocent civilians. But I get your sentiment - they've a history of doing dirty work, they're in deep already. The similarity is that their role is to complete the mission, they are trained to accept necessary casualties as a result, just never on this scale before.
Reno's turning back on orders in OG FFVII could be motivated many ways - perhaps he does just pick and choose orders, but I think he knows which orders he
can and should pick and choose from whilst also keeping his job (and, leading from that, life) - it may depend on what is being asked, and who's asking. The examples of Reno defying orders (and Rude following suit) in OG Wutai sidequest and Midgar tunnels were all post-plate drop, and perhaps that increased his disaffection for following
Shinra orders. .
I've always suspected that the plate drop was an order that couldn't have been turned down without a price that would cost them their jobs and probably lives, and your headcanon about President Shinra is fitting. In Remake, Tseng suggests that someone else would have done it if they didn't, it leaves open the question that if the Turks made themselves replaceable by refusing the mission, would that leave them replaced permanently. The Turks have their own agenda to follow, one that requires that Shinra continues to find them useful. I think Reno and Rude (and probably Tseng) each thought the order bullshit, but the consequence of not following this order would have probably been even worse (to their continued existence as Turks and period).
FFVII has so many grey areas, on one hand, the Turks are working for Shinra, they're protecting the president etc, against those branded as terrorists. They are officially sanctioned. They know they have to do bad things some times, but it could be framed as being for a greater good. Or at least that's how it might appear until they are in too deep to get out. Rude acknowledges he is a good person who does bad things during his lead up to fight with cloud for the first time. Reno echoes this, when later in the helicopter scene he says that it's a little late to be growing a conscience, showing his self awareness that their job involves doing bad things, and they are deep in already. And sure, the Turks will likely have been chosen for a predilection for being good at doing bad.
I find the Turks' plate-drop experience draws some parallels with AVALANCHE members' around the original bombing mission and casualties that ensued. Admittedly in the latter, mass civilian casualties were not part of the plan, though some Shinra casualties must have been expected, and they didn't know at the time that Shinra had a hand in the casualties that ensued. Barret in particular is portrayed as having a big heart, but that leads him to be willing to do whatever it takes for what he believes is the greater good. It's my own headcanon here, but I think drawing from the guilt over these morally grey bombing missions would pave the way for our player characters to be able to relate, empathise, and put things behind them, in a way that would have been more difficult if they had a clean sheet (and of course having bigger bad guys helps, in the enemy of my enemy is my friend way).
In Remake, Aeris saved Reno's life and recognised Rude as "not a bad person" - admittedly that was before he pushed the button (with the help of some whisper plot armor) to complete his partner's mission - would she say the same about him afterwards? She's someone who has unusual insight/foresight, I would bet her appraisal wouldn't have changed much. She has had a complex relationship with the Turks, who seem to be a buffer between her and the worst of Shinra's research goals - in a similar way the Turks also have a complex relationship with Shinra. If anyone should have a grudge against Shinra, it's Aerith, who spent so much of her childhood with her bedroom a Shinra cell, her mother being mortally wounded whilst trying to escape the facility. Yet even after plate drop, she says "the Shinra Electric Power Company isn't the real enemy. It started with them sure... but I promise you there's a much bigger threat" Aerith notably doesn't hold back when it comes to Sephiroth as being "wrong".
Why didn't Reno push the button when he had a clear chance? Did he have a conflict in his mind? Did he get drawn into a fight with AVALANCHE for personal payback, to delay his mission, both?
Rude's mad dash to push the button - what motivated that - to carry out his mission as a Turk, to recover his partner's failure, both? It looked to like his success was heavily facilitated by the whispers keeping destiny's broad strokes on track.
Rude emerges, effectively a hero to his employer, completing the mission and rescuing his partner. But a villain from the more objective perspective of toppling a plate to kill many civilians in order to frame some eco-terrorists for the crime.
The plate drop is objectively really bad. It's meant to be - we got insights into the lives of Midgar citizens intimately through the sidequests, that should make it hurt all the more. I get that many people won't see beyond the sheer scale of the atrocity. But part of what I liked about the OG and continue to like in the new one is exploring the human elements through the grey, even dark, dark grey areas. In Remake, if our player characters follow similar arcs to the original and later find ways to work with the Turks (albeit begrudgingly) for common goals, find ways to move past what's done, I'll find that interesting too.
