Look at the situation as objectively as possible.
Modern day says incest is incredibly grotesque and is looked down upon. We have further evidence of genetic failings due to lack of diversity within DNA. In-breeding just does that. The MC, who was originally from the modern world, has pre-built common sense which says "in-family marriage is messed up." I, too, agree with this, no doubt. It's abnormal; however, this isekai DOESN'T HAVE THAT NORM. The father said it himself, it's COMMON to in-breed (at least with their particular tradition). It's nothing more than a contradiction of what each person thinks is right and wrong. The sister, since birth, believing this to be normal, and that's her common sense. The MC was never like that. So it's only natural for him to be against it.
While the MC is indeed partially at fault for not putting this to question any sooner and perhaps diverging the issue, I agree with Bisami in that the father is practically FORCING him into getting married with his sister, as he tells everyone about the wedding, to specifically trap him into the situation. He's already expressed his distaste for marrying his sister, but pops had NOTHING of it. What else is he gonna do? Run away. Claim all you want about talking it out, but as the evidence stands, the father is more "you'll get used to it, so hurry up and do it" as he ignores his sons opinion.