According to my understanding, Charles Darwin was the first one to propose that inbreeding cause problems for the offspring’s health but didn’t quite “prove it”, however when this phenomena was first proposed, understood, or proven. Did it caused a reaction from the “well connected” European monarchies or from elsewhere? The ones that often would “keep things in the family”? Was there outrage to the idea? An attempt to deny it? A grim realization? Or anything on the matter?
They were certainly becoming aware of it by the late 19th century.
Princess Louis of Battenberg (née Princess Victoria of Hesse and by Rhine) had written to her grandmother, Queen Victoria, over concerns about her brother marrying their first cousin. When Victoria's brother, Grand Duke Ernst Ludwig of Hesse and by Rhine, was being "paired" with another cousin before this, Queen Victoria herself stopped the arrangement as she had concerns over possible health concerns due to their close relationship.
Queen Victoria's eldest daughter had not approved of her eldest son, Wilhelm II, proposing to his first cousin as she was concerned about the close relationship and the threat of haemophilia.
Queen Victoria's daughter and granddaughter (mentioned above) had married into the morganatic-origin Battenberg family. Victoria was glad to "have some new blood" in the family, as she realised that marrying within the same gene pool over and over had bad results.
Sources:
Letters to My Grand-Daughter by Richard Hough
Recollections: Princess Louis of Battenberg by Ilana D. Miller and Arturo Beéche