is an oblique reference literally to the degree of how closely one is related, but here refers to the concept, in Christian law derived from Jewish law, and therefore also used in civil law derivatives, specifically to the possibility of marriage with non-blood relatives. That is, affinity is in contrast to consanguinity, blood-relation, or 'strict' incest, affinity being a broader term including in-laws, and step-relatives.
AFFINITY in the proper sense the word is the connection which arises from cohabitation between each one the two parties cohabiting and the blood relations of the other. It is regarded as an impediment to marriage in the Jewish Roman and canon law...
from "A Catholic dictionary: containing some account of the doctrine, discipline ..."
by William Edward Addis, Thomas Arnold, p. 14
In the KKK passage, given the references to 'clean', 'chivalry', and ominously 'roadside parking', the usage of 'affinity' is even broader, intending general proclivity to sexual advances, or philandering.