I personally dont feel like Eri is acting out of character at all. I think the problem is that 1) Alot of anime watchers are not very observant and 2) We don't often get to see interactions from Eri's POV.
If anything Eri comes across to me as actually fairly insecure. Her "I'm a princess" act is exactly that - an act that she uses to get people to admire her. Maybe some of you can remember back to season one where they showed the episode of her and Mikoto first becomming friends - there is one part where Eri gets kind of flustered and upset and Mikoto says to her, "So you
can make a face like that". This is probably the reason why Eri and Mikoto are best friends, Mikoto can see past the facade that Eri puts up and Eri doesn't have to put up an act infront of Mikoto because she sees and accepts who she really is. It's an interesting friendship dynamic and not one that is really uncommon in real life, which is probably why it resonates as one of the more realistic relationships in SR.
Also as far as her "passiveness" in this episode... I think people are confusing her outward ojou-sama persona with her actual self. We have never seen an episode where Eri was in direct conflict with her parents, in fact the only thing we really know about Eri's relationship with them is that she is a total daddys girl :P It's not hard to imagine that she is actually a pretty devoted daughter and hence would be willing to carry out omai meeting for the sake of her parents.
One other thing that Swampstorm pointed out is also true - We have seen Eri really back down whenever she thinks that someone else is going out or is interested in Harima. The closest she's ever come to a direct confronation was with Yakumo during the school play arc and at the end she still wilted, in fact Yakumo had to say something to her (It was whispered so we don't know what evidently) to evidently keep Eri from totally giving up.
I dunno, if anything Eri comes across to me as someone who is actually kind of passive in terms of her own emotions and self interest. This is why I think she actually has low self esteem. Just compare her to Tenma who is mildly cute, rather stupid, self delusional and over confidant in her abilities. Tenma literally oozes a very inflated sense of self worth
Even when Tenma (rarely) admits her failings it doesn't really stop her from doing whatever it is she wants. Eri is almost the exact opposite of her.
This is why Eri is a tsundere type of character. The "tsun tsun" is her princess persona that she exhibts in public and the "dere dere" is her rather meek and kind inner persona that she hides from most people. It's also one of the reasons why I think a lot of people are sympathetic towards her, that is to say - her character exhibits a trait that is
very common to alot of people: She is afraid of letting everyone see who she really is.
I think it's good that she has a friend like Mikoto who is cool with her real personality, and in fact even actively supports her when it comes to trying to be honest about herself. The fact that Mikoto is all like, "So when are you going to confess to Harima" right
infront of Harima - it's not just Mikoto being mischievious, she was trying to push her friend in the direction she needs to go in to have a happy life. By that I don't mean that she has to hook up with Harima, but she needs to start actually expressing her feelings instead of hiding them behind her tsun tsun personality all the time.
Anyway, Mikoto understands Eri so why don't the rest of you guys?? To me the great thing about her character is how it's not totally contrived. Her "problem" if you will, is one that almost everyone should be familiar with on one level or another. It's not easy for people in general to be on the outside how they are internally. I think that's why the character resonates a lot with the fans. More so than say Yakumo with her psychic mind powers or Tenma having to compete with curry for Kurasama's affections. Both of those problems seem really superficial or just plain silly and hard to relate to. When you look at Eri's character however people can be like "Yeah, I understand that. I know what that's like".
Wow... this was a really long post. But seriously - I dont think Eri is acting out of character at all, in fact I think she's being very much
in character, but the debate on these boards is because maybe she as a character hasn't resonated with everyone so they are not seeing things from her perspective enough to understand how it's very likely should would act the way she currently is...