It takes about one minute after reading the question to realise the almost staggering amount of power behind the dynamics at play in this situation.
The very first issue here is how old the both of you are, how long the relationship has been going on, how serious it really is for the long term (if you're definitely planning it to be for the long term), how invested you are in the matter, how intimately you know her and her family and how intimately you'll eventually be allowed to know all of them, whether or not you're already considered to be close to the family ("part" of the "core" or actually on the fringes) and how much you know of the inherent history of the family and the circumstances / environment in which she grew up.
Not to be rude or anything, but I don't agree with "avazula" that the girlfriend standing for her own opinions on the one hand, and not having to do whatever her family asks of her on the other, are two separate issues. I don't think people's minds work in that way, the one being separable from the other.
You already have a good indication of what you're "up against": "What seems like healthy independence and personal boundaries to me, seems like rudeness to her." You state "If cultural aspects matters" - I have yet to see when it wouldn't.
As far as I'm concerned, you're actually doing exactly the wrong thing by reasoning and arguing about all of this with her. It's almost inevitable that her security has thus far greatly lain with her family, and still does. You're attacking her "comfort zone" and the source of safety she's absolutely certain of.
One thing that springs to mind, is whether you actually want her to achieve reaching her "own identity" and "learn to express herself more freely" for her sake, or for yours. For example, you're trying to compare her situation and personality with yours and your opinions about it: "Having reasonable boundaries" and "I love my parents, but I also maintain my own preferences". Here's another concern: "she doesn't seem to fully accept what I say and sometimes discussion turn to accusations / arguments". You demand from her to have her "own opinions" as far as her family or tradition is concerned, but not when it comes to her opinions regarding your opinions? Again, not to be rude or anything, but this is one of the distinctive traits of your culture.
If you're the sort of person who takes another as much into consideration as yourself, the only avenue to follow is create for her the same environment of safety and security and acceptance than she now has with her family - which'll mean a lot of selfless temporary (at least) sacrifice of your own opinions.
Once you've reached that point, she'll experience an environment in which she can freely have her "own opinions" and find her "own identity", although it seems a little arrogant for you to think that you're the one to decide / determine what that identity would be. That is, if the aim is not that she'd actually be echoing your opinions.
Whatever's going on here, you're really trespassing on anyone's privilege to behave towards their own family as they've experienced since childhood and are comfortable with. It doesn't seem as though there are anything negative about their relationship, such as abuse or manipulation or whatnot, it simply doesn't suit you.
It might help you to take a long, proper look at your own attitude in this situation.
Background to this answer :
I've been involved with three Eastern European immigrant families about three years after the fall of the Berlin Wall, through the one family's two boys - one aged twelve and the other ten - of which one was a high-functioning autist. The three families immigrated with the intent to collectively relocate in their new country for a joint purpose.
Over a period of five years, after having been one of their first contacts with "civilian" life - i.e. not officials and work related contacts - and the nature of contact with an autistic boy, I've learnt a lot about those people's mindset, particularly how close-knit the families are, how protective they are of each other - especially the parents towards the children - how much they value their family bonds and culture and how difficult it was to start assimilating in a new culture and it's social patterns and nuances - which made them even more protective of each other, even in terms of the three families guarding over each other. The thing that particularly bothered them, was people considering their culture backward - especially not being more carefree about their family bonds - and occasionally trying to convince them to "convert" to the western culture, as it were. Much of what the OP wrote, is representative of the attitude of the westerners towards them at that stage: you're rather naive, primitive and artless, we insist on teaching you real sophistication and enlightenment. In actuality, those people had human qualities which were far superior to their detractors', specifically the commitment, compassion and dedication of all of them towards the autistic boy.
Beyond that, I'd rather not expand much on having had a school acquaintance who (whilst at university) persuaded a girl whom I'd become acquainted with, to become his (first ever) girlfriend and almost unhinged her emotionally, had I not stepped in after about three months. Although she was of the same culture, actually having attended the same primary school than we had, his tactics with "grooming" the girl to his mould, are comparable to that of the OP and the author of another answer here. He apparently thought (parts of his thinking somewhat step-by-step identical to another answer here, the general similarity is almost impossible) that the right way to go about it, is applying his postgraduate engineering principles and rather callous self-imagined superior logic to a human relationship, training her like a dog to heel his step and become a disciplined housewife. I might add that after this failed "relationship", he eventually lured another girl into his web and achieved exactly that.
I think it actually takes somebody who has never been in a romantic relationship (and wouldn't ever consider it), having close to zero social skills and steering a rather bumpy ride through the world of neurotypical human beings and not so human beings, to realise the situation into which people are far too often manipulated and chained.
PS: I've just remembered a cherished expression that my former school acquaintance has often uttered - always theatrically pretending it to be said in the high art of jest (complete with fake facial expressions): If I wanted your opinion, I would've given it to you. Meanwhile, I knew him well enough by far to be fully aware thereof that it isn't jest, at all.
