I can't speak to your questions about studies done out there, but I have personal experience with this matter. I actually look a lot like my mom, but as a kid, people usually saw my resemblance to my Father first. I was told how much I looked like Dad so much and so often that my two-year-old brain actually started to believe that somehow, mom wasn't my mom.
This line of thought was discovered by my father one day when, at the mall, we went to go get the car and come back around to pick up Mom. I said, "let's not get her." Dad was shocked at the suggestion and asked, "don't you think that would scare mommy first and then also hurt her feelings if we did that?" I said, "She isn't My MOm anyway. We can just leave her here." You can probably imagine how the rest of that conversation went.
My sister, doesn't look like any of the rest of us. She is a platinum blond with blue eyes (like my Dad's Dad), while the rest of us have dark hair and eyes. and before we started fostering, people often commented on her "odd-ball-ness" with the rest the three of us with Darker features. In the end, I don't believe she has ever felt that she was treated differently by any family members. She has certainly never remarked on anything to that effect.
Maybe because of the earlier experience with me and a concern my sister might begin to believe these yahoos and think she didn't belong, maybe because this is just Dad for you, he did something that has resulted in one of those stories that now gets told over and over again.
A little before my younger sister turned three, he had had enough of perfect strangers glibly asking, "So where'd you get the blond" and when a little old lady asked the question at the grocery store he said, "The Mailman" and walked away leaving Mom standing there with the two of us girls and a shopping cart full of groceries with a look of shock on her face. The little old lady scurried away in the opposite direction with an appropriate amount of shame on her face. I was still too young to even understand what had just happened, but Dad came back seconds later and it was the first kiss between the two I personally remember seeing. Dad was splitting a gut trying not to laugh at the look on the women's face when he walked away, but still . . .
Mom and my sister have always clicked quite nicely, whereas Mom and I never have - still don't really. My sister, clicks great with Mom though and I really think "clicking" has a lot more to do with our personalities, interests, etc. than looks, but maybe there is something there. Dad and I totally click - always have. I like helping with the outdoor chores, I like the music he listens to, we have similar taste in movies and books, and we both enjoy a good debate just for the sake of debating, but we do, also look a lot alike and I've always known that. So which came first the chicken? or the egg? (well, the egg, because chickens weren't the first to lay them but still . . .) it is hard to determine causality without a wider range of experiences.
It was with family members that it was never an issue. They saw resemblances to family where strangers couldn't see any and they loved both of us girls. Then too, the family has always been inclusive and loving towards the children that were fostered in our home as well as my adopted older brother and adopted younger sister (both of which came to us after they were ten years of age).
However we looked, however we clicked, I have always known my parents loved me no matter what (except, apparently, for a few moments when I must have been angry about something when I was two). Likewise, my siblings know they are loved too and that was - and is - the important thing.