With all due respect kristyann, you sound like you've got doubts about this relationship that have little or nothing to do with his confession. I suspect there are other ancillary issues that give you pause, and perhaps he as well. I also suspect your doubts were there before he told you about his experience with his cousin. Lastly, I think you have your own answer and I would encourage you to listen to your own thoughts and feelings about your boyfriend. I think your answer about this relationship has little to do with whatever did, or did not, happen with his cousin and I think you already know what you want to do with this boyfriend.
However, to answer your question:
Would you date someone with a history of INCEST?
Thankfully my wife did not answer no. I am a survivor of incest, with both parents and my grandfather being the offender(s). If context helps, my abuse took place at a pre-school age. 23 years ago she married me, despite all my flaws, all my ugly past and all the baggage I've dumped on her the past quarter century. Thankfully she found something worthwhile in me that even I did not see. Thankfully she still puts up with me all these years later. And as I sit here, I honestly do not know why. I see nothing of value, but somehow she does.
Realize that not everyone who survives the hideous nature of incest turns around and becomes an offender. There is a theory, and one I subscribe to, that in an incestous family there are three roles: offender, denier and victim. This theory holds that (usually) one child is "assigned" the victim role. This child is usually the best and brightest, and so carries the family's pain, shame and the worst of the abuse that the offender in the family dishes out. This is the child that, if they survive, seeks treatment and most often becomes the one who escapes from the dysfunction of the incestous family.
The most common role, according to this theory, is that of the denier. These are the children (and the non-offending parent) who experience the hideous trauma and who lack the ability to deal with it. So they compartmentalize the experience: and so It Didn't Happen. These are the people who grow up and seek out dysfunctional people or offenders themselves. Because after all, Nothing Happened. Yeah right.
Then there is the relatively rare case of the offender. This is the child who identifies with the adult offender in the family. He (or she) is frightened and horrified that they are used in such a disgusting way but instead of facing it, they want to use others in the same way. These are the children who grow up to offend. These are the people who are furious at what was done to them, but instead of confronting it they cowardly pass it on. Anger is the flip side of fear, where one exists so does the other.
This is a very brief (and greatly over-generalized) capsulization of an incestuous family. This is a complex dynamic that deserves a better treatment than I am giving it.
I will say, however, that I find the title of your thread somewhat lurid and intentionally shocking. I am not offended, however I find this title somewhat in line with a grocery store rag headline. It's as if you brand anyone associated with incest with the same hot iron. Although I have literal scars from my grandfather, father and mother, I do not feel shame or embrassment over what was done. I will not accept the Scarlet Letter from anyone, however unintentional. I do not think you intended it to sound that way, however for survivors of incest it does feel that way.
As to whether he's telling the truth or not, I have no way of knowing. Nor does anyone here. We only know what you tell us. However, I suspect that there is more he is not telling you. If this is true, it most likely has to do with something he is deeply ashamed of. Whether this has to do with a real victimization of himself, or whether he victimized someone else I cannot say. Again, I think you already have your own doubts about this relationship irregardless of this subject.
Be well,
Chris