I agree with all. I have no problem with John acting the way he does for the reason you state. And although villain Arnie was really cool, hero Arnie was no less so. As you say he was reprogrammed and given new orders by young john. Villain T-800s behaviour would have been exactly like this had that particular T-800 been likewise reprogrammed. Sure he didn't happen to kill anyone in the bar scene before John told him he couldn't kill but he
was going to kill the 2 jocks later on and John had to stop him. I don't see the problem.
Another misconception people seem to have is that by the end of the film he has learnt to feel human emotion. He hasn't. He has simply learnt what kinds of things trigger particular emotions in humans. "I know now why you cry, but its something I can never do". I'm 99% certain he isn't merely saying that he cannot produce tears.
You can prefer to watch villain T-800 but as far as I'm concerned theres no basis to say that the T2 T-800 isn't believable as a Terminator.