So far I see no cons to the Ascendant Order. Sure, the team has said they do some not so nice things, that may change our minds, and the prologue they attempted to curse medallions to kill the leadership but....
How is it any different or worse than say Covenant slaughtering the citizens of Bleakrock, or the Aldmeri Dominion literally trying to genocide the Argonians, or the Pact teaming with the Veiled Heritance? (There are more examples I'm sure others could point out) The 3 Alliances have committed many crimes themselves, many atrocities unnecessary in the war.
Will the story be able to convince me that the Ascendant Order is in the worst option of the 4? Interested to see...but so far I can't see any crime being worse than Ayrenn's General trying to wipe out Argonians.