Wasn't Skynet also worried about the T-1000 becoming fully self aware and rejecting its mission? There was no such fear with the T-X.
Yeah -- the 1000 was more self-aware and had an ego.
There was the very real risk it'd go rogue and do whatever it wanted; however, the mental flexibility is what Skynet was desperate enough to rely on for its mission (longshot time-travel at the time of that movie). Though, T-800's also develop sapience once their chips are set to "write" from "read only", such as with Uncle Bob.
However, Uncle Bob may be a special case, as if we go by Resistance's canon (designed to be a prequel to the original Terminators 1 and 2), Uncle Bob was a T-850 CPU (more complex) put into a T-800 chassis, so being an 850 would explain its read/write capability, which may not be part of a T-800 CPU.
Double however, it looks as though T-800's can also do this anyway over time by itself ("neural net learning processor") or by manual switch, which is a... massive flaw for what's supposed to be a mass manufactured battlefield machine.
IIRC, in extended media there were cases where T-800's that survived on the field long enough became smarter and more adept, salvaging parts, adding modifications to their chassis, and even going rogue.
We don't know if Pops were set to read/write before it was sent back to protect Sarah, or if he developed sapience over time, but there's no doubt he was fully self-aware, had emotions, et cetera, over the decades. "Take care of my Sarah."
Carl was most likely not put to read/write by Skynet, though he and the other infiltrators (mentioned in the film, destroyed by Sarah via coordinates sent to her by Carl) sent back may have been set to it as a "fuck it, why not?" option by Skynet because of how badly things had gone: "It couldn't make things worse, right?" and all that jazz.
He developed sapience after, well,
thinking over years. Then again, Dark Fate was a dumpster fire that makes Aliens 3 and Resurrection combined look like marvels of cinema, so... shrug?
The T-X was highly capable and intelligent, and it did display emotions (fear, surprise, annoyance, anger, et cetera), which is what the T-1000 displayed, too. That implies sapience, not just sentience.
