@UuulonnyuuU
To be more accurate, incest is basically inbreeding where the possibility of recessive alleles being paired increases. (Meaning that if there is no incest, you will just have a lower chance of getting paired recessive alleles)
Humans have some types of recessive alleles that can be dangerous, beneficial, or do completely nothing if you have two copies.
If they only have beneficial recessive traits, then incest isn't a big problem.
In a normal population, if they commit incest for thousands of years, they would either go extinct or lose the dangerous alleles as the ones who are born with them die and don't reproduce. (By this point, incest is no longer harmful)
The drawback is that they would lack genetic diversity (AKA, they all are almost the same genetically, a virus could easily wipe them out or they would be less likely to survive in other environments)
Mutations can occur regardless of whether there is incest or not. (Also can be good, bad, or nothing)
I don't know how this would apply to an immortal family line descending from a god in a fantasy world since there isn't any scientists or magician publishing any peer reviewed articles on the manner, so take all of this with a grain of salt.