There are two levels to my personal experiences: race as related to culture and lifestyle, and race as related to outward appearance.
Regarding race as related to culture and lifestyle, I feel out of place because each of my sides live their lives differently, neither of which exactly fit me. A lot of people don't understand when I say I feel like I don't fit in anywhere. I guess it is hard to understand unless you personally experience it or witness someone else experiencing it. It's kind of like straddling two worlds and wishing someone else had the same combination. In this sense, it's similar to immigrants coming to the United States, and having children growing up surrounded by the American way of life but also surrounded by a family that lives in a different way and has different beliefs. It's not unlike Anzaldua's "mestiza consciousness," where she straddles two worlds and so creates a third identity to reconcile them. If you hang out with one side, they're kind of like you in some sense, but not fully, and same with the other side. In my case, I can hang out with other Muslims because they also don't drink (which is something you don't always get on the other side), but I still don't quite fit in because I didn't grow up going to the mosque for Sunday school (only for a couple years) so sometimes people will talk about things that I have absolutely no clue about. And my lifestyle choices are not always the same because while the traditional thing to do is have an arranged marriage (though this isn't always the case anymore), it's something I definitely would never do. But on the other side, it's the same thing: in some ways you fit in, but in some ways you don't. But, this isn't always to do with race, it's just the culture that comes along with the race, so as I said earlier, this is something that is experienced by children of immigrants living in the US, and people of a certain religion that aren't as "religious" as others in the same religion. So, this point isn't necessarily about race exclusively.
But regarding race specifically, there are some challenges as well. It's frustrating when people label me as "white" just because I'm light-skinned. I mean I guess it's a fair assumption to make, especially from afar, but if you compare me to a true "white girl" there are significant differences, so it's not fair to label me as a person that I don't always have much in common with. People who do that have no idea who I really am, how I've been raised, and how I live my life. It's happened to me so much growing up that I internalized it. In my Race, Class, and Gender course 2 years ago, we had to write a Racial Identity Development paper in which we discussed our experiences of racialization throughout our lives. We first had to pick whether we identified ourselves as white or as a person of color. I immediately decided I was white (based on the white privileges I've had), but then thought twice after speaking with the professor and realizing I had experiences as a person of color also (since my name and facial features are often non-white indicators). So, after discussing this, I argued in my paper that I am sometimes white and sometimes a person of color, depending on the circumstance. This is not how I feel about myself (I just like to think I am ME), but rather how others have perceived me. Since the world doesn't do so well with these fuzzy in-between categories (we like to place people into categories, hence the black/white racial dichotomy) I am put to one category or another, but you can never be BOTH at once. (I mean hey, that's just asking for a little too much). It gets a little tiring when people try to tell you who you are. I remember when I was younger, some friends and I were all deciding which Disney princess we were most like. I thought that I was Belle from Beauty and the Beast (brown hair, light skin), but another girl told me I was Jasmine from Aladdin. Though she didn't state it blatantly, the underlying (subconscious) message she was sending was, "you're not white, you're brown." Um thank you, for explaining my identity to me.
When I was younger I always considered myself to be white. I don't know why, I felt more drawn to that side I suppose. It may possibly have something to do with internalizing how people perceived me, but I haven't explored that possibility fully just yet. But as I've gotten older I've tried (and struggled) to embrace both sides. As of now, I just consider myself to be ME (and my particular mix), rather than trying to say I identify with one side over the other (I really can't stand getting that question, it happens way too often).