I believe there are two main genetic arguments against inbreeding: increased prevalence of genetic defects and decreased adaptability.
The first, if the two have any such defects to worry about, should hopefully sort itself out in a few generations of the carriers dying, since there doesn't seem to be much in the way of lifesaving equipment to prolong their lives until they have children. It is unfortunate, since the vast majority will probably be lesbians (which I hear is at least partially genetic), but that is what happens to isolated groups on earth.
The second is not a problem at all, since they are living in a nuclear wasteland, which is constantly granting everyone new genetic mutations that might prove useful (if not lethal), thus keeping the gene pool fresh.
In conclusion, eventually, the earth will be covered in lesbians.
