Incest was definitely a "big deal." The issue is your definition of incest is different from theirs. You won't find any parent-child or brother-sister relations on Charles' family tree, just uncle-niece and first cousin relationships.

Consanguinity, or marrying relatively close relatives like nieces or first cousins, required a special dispensation from the Church that may or may not be forthcoming depending on your relations with the Papacy.

Famously, Henry VIII of England won a Papal dispensation to marry his brother's widow Catherine of Aragon even though such a relationship was incestuous legally, then later petitioned for a Papal dispensation to anull his marriage with Catherine...because she was his brother's widow. The Church did not like this suggestion.