The Synagogue is already there as you say but will be replaced by a much smaller one I imagine. The whole project is a monstrosity and Manchester City council should hang their heads in shame as part of it.
It does look pretty horrible, and will overshadow some nice buildings in that area (not just the town hall and library). I'm sure that something more aesthetic could be put there, but the area currently isn't great either, so something needs to be done.
I know tall buildings hugely split opinion, but I think Manchester has a great mix of new, 60's/70's (not much good there to be honest), and old, and the rather chaotic nature of it all has its own charm. Modern cities built new and tall can look great, but they often lack any real character, and whilst its a shame to lose some of the old pubs, some aren't worth the bother, I've walked past that one fairly regularly recently, and it wouldn't entice me in as it is.
Manchester is a great modern city that still has its character, a character than can be modernised tastefully if the people in charge do it right, but modern tall buildings certainly have a place within it, and are really the only way the city centre can continue to grow.
These don't do that, so as residents of the city (I'm not), people should object to them in the right manner, no matter who the names fronting the development are.