I thought cole's approval for choices was the most random, i guess since he is a spirit it's understandable as it's sense of morality is far different.
even though the seekers were corrupted she didn't want them disbanded, even though the chantry is practically destroyed she doesn't want it abandoned, so I think her views of the templars is the same, she would want them restored not disbanded. So I don't think disapproval for that action is out of character for her.
I don't see it. Her being angry at the templars is =/= you deciding to disband- practically removing the templar order. Cassandra has great amount of respect and love for the templars, of course she'd disapprove.
Cassandra suggests you disband them. I can keep repeating that as many times as necessary. If she didn't suggest it, I wouldn't think twice about how her approval is scored for disbanding them, because while she is all about Tough Love (she does, actually, consider that maybe the Seekers should be disbanded as well), I would've assumed her Tough Love only goes so far. Hell, the first time I sided with and then conscripted the Templars, I didn't have her with me, so I didn't think about her approval at all.
But the next time I went through that quest (with the intent to keep the Order together), I was surprised to hear her suggest I do the thing she had so strongly disapproved of. During the quest, she is clearly horrified by what's happened and how thoroughly corrupt the Templars have become (not surprising), and she specifically says they should be disbanded and absorbed into the Inquisition (not entirely surprising either, really). Because as she herself says, we don't the institution, we just need the Templars. Her Greatly Disapproves when you actually do it makes no sense when you take that into account.
It isn't just "oh, she's mad at the Order." It's "she has an extremely strong reaction to the events she's witnessing, AND ALSO suggests a course of action she feels would be the correct one." Like I said, if it was a milder disapproves, I could rationalize it in any number of ways, from her self-doubt to her fear of the Inquisition being misused, etc. But Greatly Approve/Disapprove seems to be reserved for really, really defining characteristics, and it seems really strange for the otherwise very say-exactly-what-she-means Cassandra to contradict herself so completely.