Well, that's my point; this is a characterization of Babs that's wildly in contrast to her established habits under years of other writers (even Morrison, for whom characterization seems to be a fairly low priority). It shows a lack of respect/interest by Loeb in Oracle and her current canon or character, which makes it impossible for me to buy the Kara-Babs teamup here as coming from any kind of authentic respect for Babs either.
Krypto didn't like her! Did they ever explain that?
Krypto doesn't like anybody. (Except he likes Diana. But everybody likes Diana. I will credit Loeb with some amusing dialog exchanges.)
Actually as much as the Supertorso introduction is forced and ridiculous and other increasingly melodramatic adjectives of disdain, that part basically works for me, at least on a conceptual level. Clark is a trusted and respected member of the superhero community, and he vouched for her. When Superman says "this is my cousin, she's cool," you aren't going to see many people have a problem with that. And those few who you'd expect to need more than that (Bruce and Diana frex, or those less part of that community, like Grace) were generally the ones who did.