I have no problem with the chip removal scene. That makes perfect sense to me. The Resistance captures and reprograms the T-800, it makes sense that since he was basically a grunt, his chip would be preset to read-only. He was taken from the cold storage facility in haste, afterall. Even though I don't mind the scene getting scrapped for "the more contact I have with humans, the more I learn", I dig it. It shows Sarah's prejudice against machines and John Connor's authority as a leader.
Glitchy T-1000 is a completely different animal. Cameron says that he wanted the audience to think the T-1000 was unstoppable and had the upper hand, not that he actually was. That's to evoke a feeling, not cut down on time. The trimming of scenes happens in post-production. Why didn't the T-1000 run you ask? Because during the shooting script, story boards and film he was glitching due to the liquid metal bath. It effected him. Same reason why the Endo doesn't just run after Sarah and Kyle in the first film, he just got run over by a tanker and got his skin blown off. He's a slow, limping mess (but thankfully, so is Kyle . . . just like Sarah in the second film). Cutting that doesn't just negate it. You can see several times where those glimpses of the glitches would take place. For instance, T-1000 walking. We see that in the theatrical version and we can even see him going to touch the yellow and black rail. Just because it was deleted, doesn't mean it didn't happen. It's not like the garage surgery scene where a line is added that negates the deleted scene.
T-1000 was ****ed up, that's why he was walking. Cameron cut it, not because he didn't want T-1000 glitching, but so the audience would be more fearful for the heroes (even if T-1000 beating down the T-800 with that rod would be enough). The fact you acknowledge the theatrical versions subtle "blip" glitch shows that he is glitchy regardless, so, nuff said.
If we go by your logic, because the gift giving scene in the Fellowship of the Ring was cut, I have to assume that the Fellowship obtained their new green cloaks when they took a ****. Aragon got his dagger that he uses throughout the trilogy from pulling it out of his ass, and Merry and Pippin's daggers and wee belts, well who the hell knows where those came from.