Did God allowed incest before? Did Noah and his family committed incest? If yes when did God start forbidding it and why? If no, how did Noah and his family repopulate the world and how about the risk of genetic diseases caused by the inbreeding?
No one is to approach any close relative to have sexual relations. I am the Lord.
Why was it forbidden? Possibly because of genetic problems that occur in offspring of close relations, though that is speculation - that chapter does not give any general reason.
1 As an example, Abraham was married to Sarah, his half-sister.
The passengers on the ark included three sons of Noah and their wives. The next generation of the family would be first cousins. Even leaving aside the fact that the Law came long after Noah, first cousins is not one of the forbidden relationships.
Plenty of places permit marriage between first cousins even today; the US is relatively unusual in forbidding it.