My experience is that there was no objection made. I think I have detected a number of cousin and cousin-once-removed marriages in my ancestry, and so far have not come across any record of objection. I think sometimes it was encouraged in order to return a farm to the male line, or to keep a dowry in the family.
I have one case where there were three marriages involving close relatives in adjoining farms in as many generations - eventually the desired-for union of the two properties ocurred. Cannot vouch for the genetic impact.