I would say, that a child should be raised to be able belonging to the culture, where it is supposed to live (that is "C") as she will be interacting with it until adulthood (and potentially be able to choose for herself, where she wants to live and what culture respect) as well, as to the culture of their parents (which is her heritage) - in your case it looks like you chose to belong to culture "C" too, and not follow culture "N", so the choice seems clear to me - both by living there and following parents she belongs to culture "C".
Even if you were raised in culture "N" and it affects you in many ways, you willingly moved away and see it as something you do not want to belong to. You dislike culture "N" to that point, that you willingly dropped part of your heritage. It is your choice and right (and who I am to tell you what to do anyway. But I agree with your move.) You see "N" as toxic, would you feed any toxicity to your own child? Especially, when you moved away from "N" to have your child not affected by "N"?
Yes, if you look different, then average people around you and your child would probably look different too. So what. I think, that she should know, that you were born in another country/culture, as well as why you moved out and chose current as your preferred. If somebody will ask her "where are you from? where are you really from?", she could proudly state
I am from here. My parents worked hard to get here and became part of great culture C and I am part of C longer that I live!
Yes, you should tell her, that you are from "N" (she will discover it anyway and probably sooner, than you will want, if you try hide it) - and it is much better, if she knows that from you (and your point of view), than if she is confronted with it by somebody else (and probably with a lot prejudice against her) and then realized, that you lied to her all the time (or at least mislead her) and lost a lot of trust in you. But while you tell her, that you are from "N", you should also explain to her, that you went away because it was just terrible and toxic and you did that to become part of C and give her the priviledge to be part of C. Then, when somebody (inevitably - in any large group is somebody say "not ideal") put it against her, she would answer like
I know, that my parents were born in N, while I was born here. You would not believe how terrible it was there and how we are all glad, that we do not belong to N but to C. Do you not think, that C is much better than N?
What is then the point about bullying here about you being from N (which is bad) and implying, that she is N too? She is C, and totally agrees, that N is terrible and her parent did the best to leave N, cut the ties and become C too.
You will teach her anyway a lot of things about places and histories, as you travelled extensively and you can tell here a lot about many countries. If you can not find anything positive about N, that is part of the larger picture of the world too. I would not concentrate too much on N (as forbidden fruit tastes the best, but rotten apple is just plain awful and untasty), just take it for granted, that she knows what was terrible there and why it was terrible. As well as what was good and bad in other countries you know about and why that is good and bad. And also and mainly what is good and bad about C and why it's good and bad and why it is better, than anything else you know about. (That there is something bad in ANY country IMHO goes without discussion, but it goes with everything, nothing is 110% perfect, 90% or even 80% is good enought usually.)
Well, I was raised in a not totally evil country, but bad too, I was taught to say something totally different at home (which was true) and totally different in school and public (which was many lies), as publically saying true or asking "inappropriate" guestions may put our whole family in danger. It was not a good feeling. And of course I was not told everything (a child cannot be trusted so much, that would not fall for sophisticated trap), so as I grew, I was told more and more by my parents. When the situation started changing in our country, my parents actively worked for the change and I contributed a lot personally, and finally the change came (so we transferred from N to C without physically moving). We could be severally charged for what we did before and during the change by the old regime (to the point of having our lives destroyed as well as lives of our friends and relatives) while it would not be even offense in other states. Many years after the change I still learn more things I did not know and how bad the situation was. I am glad I was not forced to put my childern in the same problem and that they could be "part of C" from birth. I do tell them, why our "N" was really bad and should not happen ever again and I think it is for their best to be "C and just C" but know, that part of our family history was being under "N", and that it was bad and that their heritage is the "C" I willingly fight for and accepted, not the "N", which was forced on me by the fact I was born at some place in some time and that I then put away as much as I could.
I am more afraid of the fact, that many people around just forget/were not told about the true nature of N and that some young think, that it may not be so bad, if someone tells them some half-true or carefully selected nice points or even total lies how N had "also good sides" (yes, it is true, that basic food was like 5x cheaper back then (in nominal value), but it should be also said, that even the bad paid now brings home like 15x more, than was total average back that times, so they can buy more than 3x more of food, from their salary. And also that there is abundance of basic things (like toilet paper), while back then it was many time a problem to find shop, where it actually was and if you find one, you had to buy as much as you could (which was limited too) to have some, until you find another shop with it, not as today, whe if you want it, you go to any shop any time of day and week and buy how much you want and can choose from many kinds. And you are sure it would be so in future too.)
So heritage of my childs is, that their parents actively selected C to escape from N and that N is just plain bad and wrong under any disguise (and why). And the "very arbitrary, authoritarian and absurd" traditions of N are just wrong - with much more concern put at why anything like that is wrong, than on detailed description of what such tradition tried to present.
(Not sure how to describe that, but let's just say I do put more effort in telling them, that everyone should be valued by what he does and that while there are some differences between boys and girls (boy cannot become pregnant and so deliver baby, and average boy is little more muscular and larger than average girl, but the difference is not so big, so there are many girls, who are stronger that some other boys, or larger), that there actually are nearly any activities, where one dedicated person could not be more successful or better or how you want to put it, than average person of other sex. So in marriage they both have equal rights and (except pregnancy) there is nothing, which one can do and the other cannot. I am a boy and I was totally able to take fully care of children while my wife was away from home even for many days. And it is not unusual to see me sewing clothes or cooking, while my wife works on computer. Or I am working on computer and she cooks. While we have a different style of cooking, it could not be said, that one is better than the other, be it from gastronomical, nutritional or monetary value. Big decisions are made together, after discussion, even the children can voice their opinions (while it does not have the same weight as they do not bring money home, it is still something, which is taken seriously) and the result is something agreed on. (be it we will buy that new car together, or be it I will by this tool for my hobby and you will book that travel for your pleasure). Also I and my wife do both work (so bring money to common home), but when she was with small children at home, it was considered as exactly the same value as my work pay - if she would not be there, I would be there, so I will work the hours less and my workpay would be so less - so the price of her work was exactly the same as the price of my work, as without it I would not be able to do the work.
So as result saying, that model, where man rules the family and women work at home and obeys him (based on that the man is more than the woman) is just obviously wrong, as it can be seen, that we are a happy family and we both are equally important and all major decisions are made together and there is good reason for it. Also it is obvious, that we both are equally able to do housework, cooking and such. And as only woman is able of pregnancy, it is her work to be pregnant, while my work is to support her during the time as much as I can, because she does something I am not able to. After giving birth there is a period, where her body is in weakened, so she had to rest and only she is able to breastfeed children, which is better than artifical feeding them, so she still has to do that and I have to help as much with which I can (like washing children, textiles, cooking and such) until she is physically able to share some part of that and when she stops breastfeeding we can consider together, how to arrange our lives, so both of us can spend time with children (and each other) and what part of housework (cooking, shopping...) and paywork each of us would do in respect to help our all family best.
If our children live in such an environment, they just see that it is so and saying that strict partriarchy and woman being just "housekeeping slave" is just stating the obvious and it may even look un-understable to children, that there are places, where it is otherwise.
So show her (or later them), that the C model is "good and natural" and if you later describe her why N model is just bad, she would see it's obvious a will be glad, that she is born "C".
No need to go all the details, how grand-grand-grand-something did it the way, that today is visibly nonsense and that she should so do visibly nonsense just because hundred years ago in totally different country some (maybe fictional, or misinterpreted) long dead authority just stated so.
In other way - there are many countries and cultures. Now we live in "C" which we believe is best and its history and roots are such and such (with lot of details), there are also other countries like A, which have such history and roots and is good in this and bad in that (with some details) and B which has others and is good and bad in others and N which has totally diferent and have such history and roots and we had the bad luck to be born there because its state is really bad, so we had to work hard to go away from that to live in some sane country. We are glad, that we are now part of C.