This was a question I wrestled with a lot. When I first started TTC, I lived in Toronto, the most racially diverse city in the world. I'm white, my family background is in part Acadian.
When I turned to the sperm bank, I wanted to stay away from Acadians and Ashkenazi blood lines, because of genetic issues, but I later had an Acadian/Ashkenazi panel run, and it turns out I'm not a carrier for anything diagnosable (I.e. CF, Tay-Sachs, and I don't carry the BCRA1 or 2 genes) so that became less of an issue. (Acadians and Ashkenazim have higher rates of some recessive genetic disorders, because both groups have historically been endogamous.)
I had a similar experience to what AngelaM relays, talking to a couple who were fellow TTCers who were both biracial about the scarcity of donors of colour who were available in the US as "Canadian compliant" or available through the Canadian sperm bank made me realize that I could add "I can easily choose a sperm donor of my race" to my white privilege knapsack.
Like Kwynne says in the other thread, race being "one more thing" for my kid to handle did cross my mind, but after I thought about it a bit, I decided that my ability to pick and choose how my kid deals with race is a reflection of my own racial privilege as a white person. I.e. unlike Kwynne, I can choose whether my child will be white or not. The "one more thing" bit bugs me in a way I can't quite explain, and I decided it didn't come down to that.
I'm a single parent by choice, I'm trans, I'm queer, I'm kinky, I'm a non-resident temporarily residing in a very white part of the United States - my kid will have a lot to deal with, and, likely my kid will end up with siblings who are not the same race ze will be, because I plan to adopt, quite likely from foster care, at some point in the future.
But, I am all of these things - and my family is all of these things - at the same time. It's all tied together. The possible future of my family as a multiracial family is not "one more thing" it will be part of who and what we are.
In my deliberation process, once I felt I had run out of known donor options and turned to the sperm bank, I heard it all - choose a black donor, they probably have better sperm. Ethnic babies are the cutest! Won't your kid have enough to deal with? What do you know about raising a child of colour? You speak Spanish! Your kid can take violin! Asians are good at math! etc, etc, etc.
I got a mix of comments - some advocating I choose a non-white donor, some advocating I choose a white donor, some advocating that I just choose a donor and pretend race doesn't matter. Actually, they didn't want me to pretend, they wanted me to believe it.
The thing that all these comments had in common was they were not antiracist, and many of them were overtly racist and/or propagated racial stereotypes.
I decided that when it came to choosing a known donor, race was less important than the donor and I being on the same page politically and around parenting and what roles we each wanted. Really, my priorities were - HIV status, other STDs, politics/expectations/etc, medical history, and then race.
However, because of the scarcity of donors of colour, and because it bothered me that I could pretend that race didn't matter, I used race as my first criteria for narrowing my sperm bank selection. As my doctor said, ordering from the sperm bank was easier than ordering pizza.
At first, I thought this might limit my options, so I looked at all the profiles, regardless of race, but if I remember correctly, at least 80% of the donors were white. Maybe more.
As it turned out, I didn't get pregnant with the six vials of donor sperm I bought (I chose a donor who was white, blond/blue or green, I don't remember, and tall).
Known donor search number two yielded two known donors. I haven't (yet) gotten pregnant with my known donor - he's also white. I also talked to another white man, a black man, and a latino man, and eliminated each because of issues that had nothing to do with race. I also chose another known donor, who was also white, but we had scheduling issues.
However, my decisions would have been different if I had a partner who was not white and it was possible for us to obtain a donor who would make our family "match" with regard to race if we decided that was important to us. I have to say, if I were partnered and not carrying the child or not using my gametes to conceive, the "matching" idea would be very compelling for me. Because of the way race works in society, any child who is part white is not seen as "part white" but rather as "black" or "half latino" or "half asian" and so on.
My decisions would also have been very different if I was not white.
Finally, in Canada at least, a counselling session is mandatory before you can order sperm from a bank. I went through it twice, once with my doctor, before my first order, and later, with a counsellor at a fertility clinic. The counsellor seemed visibly relieved when I told her I had already picked my donor and that I had matched him to me in terms of appearance. That's what she counsels single parents by choice to do - find the donor the most like you. I got the sense that she explicitly discourages people from choosing donors across racial lines.
I'm sure that situation would play out very differently for a single parent of colour.
Ok, that's my ten cents, but I've got at least another dollar's worth of thoughts on race, donors, and parenting.