IDK, this is touchy for me because I am Caucasian & my husband is African American so I have personal experience with this one.
OK, you have a whole bunch of stuff going on here spinning off of this one thing. It sounds like you don't want your daughter to have a boyfriend at all, never mind the race, correct?
Let me ask you this: why do you care what other people think if your daughter doesn't? I mean, if you're truly not a racist as you say, then it shouldn't matter, right?
In my mind it all comes back to how you're raising your children. My parents raised me to believe that skin color doesn't matter one little bit. I dated white guys exclusively up until I was a senior in high school. For a while I dated an Iranian guy, and my parents never said a word about it. Once I got into college & around a more diverse group of people I dated a couple of African American guys before meeting my husband. When things were clearly serious between us my mother pulled me aside & basically said that while she would never tell me who I could/should/couldn't/shouldn't date, she wanted me to think very hard about choosing someone of another race to marry because her opinion is that married life is hard enough without that added into the equation. She was also concerned about us having children together. I told her (at the age of 21) that we were strong enough to be able to handle anything together. He & I are now 35 & 34 years old respectively and have a 12 year old son and a 10 year old daughter together. Yes, over the years we have had issues crop up based solely on our race as have our children. It is an extremely unfortunate part of our lives, but you know what? We're ok. We're stronger because of it. We pull together & defend ourselves, our choices, and our children. We have taught our children tolerance, strength, and determination at much earlier ages than I imagine other children would have been introduced to such ideas.
Decide whether or not this is something YOU are strong enough to handle because clearly your daughter can. Then, once you've figured that out, if the answer is a resounding yes, then tell anyone else in your family who has an issue with it to go screw themselves.
**ETA** My maternal grandparents were absolutely racists. When my mother told her mother that I was marrying a boy named Shannon, my grandmother was so very pleased to hear I'd be marrying a nice Irish boy, lmao! They were in for a rude awakening & I know my mom was nervous to tell them the actual situation. I assured her that they would be fine with it, but if they were not, that they could plan on not seeing me again as long as they lived because Shannon & our (at the time) unborn child would be my family forever more. At well over 80 years old, they came around & loved both my husband & children with all of their hearts. This proves to me that you CAN, in fact, teach an old dog new tricks.