Sounds like you feel the need to live in a more like-minded area where you would get more support for your parenting style. Depending on your circumstances, there are many places where you would feel welcome. Don't expect your views though to be 100% with everyone, even in a more diverse community. Just somewhere that doing things in a non-standard way are generally okay.
The ethnic issue is separate. If you have no real connection to what your background is, than so be it. Don't feel an obligation to form an alliance unless there is a specific reason. This would be for instance, if you married someone from your bio background (which you didn't) or had religious ties (which I think you would have mentioned), etc. You had a white-oriented upbringing. It's no sin and nothing you should try to distance yourself from. At least your own child will have you to relate to (a luxury you didn't have yet survived!)
I too was raised by a step-dad after my own father died when I was 10. While I maintain ties to my father's family, and share a religion, I am still very close with my step family (ironically, I only ever knew my grandmother from my mom's family and no one else). I love both "sides" of my family, but in different ways.
On an amusing note, I actually look like my step dad and NOT my bio dad, which lead to some interesting questions growing up, plus the fact the step dad is much younger and all of the above are white. I ended up explaining things often but I only dole out the needs-to-know info as required.
I grew up physically closer to my step family but ended up marrying someone more of my dad's background. Now my children play with their cousins and we spend holidays with them... Everything's zen.
The fact that I didn't look like my dad or his family, and now have children who bear no obvious connection to me has never had any negative effect, except for the rare odd question. My in-laws find my non-traditional background a bit off-putting but I simply get off the subject if they start with the questions. I try to "make up" with it elsewhere, by example, showing interest in their history and culture.
I find I have more in common not with necessarily people of my same background but those who also grew up in non-traditional households and those of mixed backgrounds of any sort. What is funny is that we don't necessarily sit around and talk about our mixed backgrounds but we're drawn to each other none-the-less. My kids too, seem to have plenty of mixed friends, either racially, nationality and/or are also bilingual, etc. I have them in a very mixed school and they are very comfortable.
I even considered putting them in a special program for children with similar backgrounds (growing up with English and French) but I thought to myself, looking over the sea of white faces, with only a few token exceptions "Oh this isn't the diverse atmosphere my kids have now..." My son passed the exam... and to everyone's shock, we then turned down the place! (there were a few other issues too though).
Go with your heart on this one. The fact you don't feel connected to what I'll bluntly say, what you look like, is of little matter. You don't have to raise your child somewhere were there are necessarily a lot of kids exactly like she is but just somewhere that being a little different is not necessarily anything bad.
I once asked my sister about a mutual friend whose dd was the result of a visit to a sperm bank. How does she handle the whole single mom, who is the dad issue? My sister laughed. "Well, the girl next to her in class has two mommies so..." As long as she's not the Only One who has something unusual, she'll be fine!