I cannot believe this is realistically being discussed. I'm truly in awe. My initial reaction is "HELL NO".
But, in any argument, I imagine the extreme example of the opposing view and decide if, in that case, it shouldn't be permitted then it's not a matter of 'if it should be done', but rather, 'when' it should be done.
So I'm going to play my own devil's advocate and make an extreme example: A brother and sister want to have a baby. Do we as a society have the right to refuse them this privilege? Yes, I believe so.
Though this isn't giving a 'license' to have a baby, it is restricting some from having children and not others, which is in essence the same. (?)
Now I'm trying to think of all the ways that this is different from other situations in which I wouldn't think it's appropriate to restrict one from having a baby.
An obvious difference is that they're related, ergo procreation will cause DNA mutations in their children. But isn't bad eye-sight a DNA mutation? Isn't being too tall or short a DNA mutation? There are literal thousands of DNA mutations. Is it a matter of the severity of the mutation? How is that decided? Perhaps my knowledge is simply too limited.
Another obvious difference is that we as society reject the thought of incest. But I outright reject the idea that we should reject any privilege on that premise alone (societal discomfort).
Are the rights to any others being infringed upon? Perhaps the right to the pursuit of happiness to the handicapped children of incestual couples. But again, this gets back to the root question of what's the difference between this situation and other situations?
I will stick with my answer in a most uncomfortable fashion because I cannot give a logical reason why. The fact is that I do think in some cases, procreation should be limited. But I do not believe the government should impose its will, whatever its will may be, without just cause. Just cause being the infringement on the rights of others. So my beliefs are contradictory and I'm having a difficult time at the moment in rectifying that.