Yeah I never get the hate either...the Chantry has negatives (Exalted Marches and treatment of mages) but the Qunari are a thousand times worse on both regards and everyone loves them. Hell, the Chantry doesn't even care about most the social issues that people give real organized religions flak for.
Yes it does - It has reverse sexism (the catholic church gets flak because women can't have any higher office, the chantry just reverses this: men are idiots that can't have any office, they can be brothers and that's it!) for example
It represses minorities (elfs, dwarfs etc. - and: mages as you already stated), it influences politics (which religion should just not do, separation of church and state was developped for a reason...and in a lot of states that is still violated today and leads to such stupid decision like allowing male genital mutilation (circumcision) without any medical need (religious reasons or even aesthetic ones (!)), while punishing female genital mutilation - talk about double standards!), it threatens and kills people (seekers, templars and spies/assassins like Leliana) for religious reasons and it has it's own zealotish bullies (the templars) and it deals in drugs (Lyrium is essentially a drug...one that can be used for good by mages, but that's it, all other people are harmed by consuming it) and brainwashing (the people of Thedas against mages, mostly of course its own templars!), it destroys countries that don't comply with its wishes (the Dales!) and it preaches stuff that can't be proven (the creation of the Darkspawn by Tevinter magisters entering the black city...hell, most evidence points to the city being black already when they got there!) etc.
Yes, it does some good - but it's hopelessly zealous and backward in its methods and inhibits science (like the catholic church did and sometimes still does, by voting negatively in ethical commissions)
Note: I am a non-believer that's probably why you will never be able to convince me religion is good for anything (it's a delusion to me) - but I am normally not an "in your face" guy that belittles people for believing (I do feel sorry for them sometimes, but still, I see no reason to make fun of them) and that's why I can watch religions without much bias (I can say that the churches do some good (maybe even a lot - like in chantry does in Thedas), but that does not excuse the flaws they have and the scandals that are swept under the rug (white washes!) or just forgotten very fast (like the child-sexual-abuse in Germany and other nations, that is treated like it has never happened, just because the last scandal about it was a few years ago - they even had the audacity to shut of the abuse-hotline they created exactly because of that scandal barely a year later...) - that's why I don' like church, because no matter what good it does, as long as it has this much power, influence, money it is a danger to modern life for me, mostly because the organisation is never held accountable for what havoc is wrecked by its clergy (just like the chantry in Thedas, though they still have more influence...hell, I would not be surprised if the upper-level chantry sisters (revered mothers and above) do have sex and maybe even have families, just like the bishops/popes of old did in the catholic church!)
greetings LAX
ps: I want the separation of church and state inforced and religions to not be given tax-breaks anymore (!) - but I don't want religion forbidden (it just has no real place in the public sphere IMHO)