Doesn't even have to be emotion/morals.
Remember, the T-800's can be programmed to follow orders, and to do so to the letter. Obviously Skynet is the one giving the orders by default, making it so that the T-800's (and previous models of course) have no real free will... but what if a newer model, the T-1000, was impossible to program in this way (due to the complexity of how it works)? It might not take kindly to the idea of being slaves to Skynet.
Of course emotions/morals might follow, but I think an interesting aspect could be to keep that back for a while... make it a kind of creepy alliance to make.
It would bring questions like "What happens if we help the T-1000's take down Skynet? Will they turn on us once Skynet is destroyed? Will we have exchanged one enemy for an even worse one?" to the forefront.