Hello! Please remember that my response is for information only, we are not establishing a therapeutic relationship.
This sounds like this is a very difficult and painful issue that you have. The problem, though, is that no matter what woman you date, she is going to have stories and issues from the past because she will have had a life before meeting you. So unless you address whatever issue underlies this problem for you, it is likely that you will have this problem over and over again.
The best way to address this issue would be to enter individual psychotherapy where you can really explore where the issue comes from. Keep in mind that anger and resentment are what we call "Secondary Emotions," meaning that there is generally a deeper, more vulnerable emotion that lies beneath these feelings, it is some kind of pain. You'll need to identify the specific nature of that pain and process through that in order to be able to let go of the anger and resentment that comes up when you learn about a girlfriend's history.
A really good website to look for a therapist is www.psychologytoday.com, where you can look at pictures and profiles of various therapists in your city. You can also try www.therapytribe.com
I hope that this helps. I believe you can address this issue, but first you need to understand it more fully.
I am not familiar with the culture in Ireland. Biracial couples are quite common in the United States, so your comments would generally be taken as offensive by many people.
So, given your strong viewpoint, it sounds like you have no choice but to break up with this woman. I don't see how you are going to move beyond it unless you were to change your core beliefs about white women and black men, which it sounds like you do not wish to do.