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The game tracks paternity "under the hood": if a child is a product of a torrid love affair, their "father" isn't actually their father. However, the inbreeding warning you see in the marriage menu doesn't go by the father listed on the character page, it goes by their real fathers. IIRC, the game checks for any common ancestors up to 5 generations, going by mothers and (real) fathers. If the common ancestor count is greater than 0, the warning shows up, even if none of the official fathers are related.
For this reason, I would recommend ignoring brownacs' advice. If you keep marrying together people that are only a little inbred, you will eventually end up producing people that are very inbred, because the common ancestor count will steadily climb. The consanguinity doctrine of your faith does not check number of common ancestors, but instead familial relations, ie, cousin marriage does indeed allow cousins to marry.
Personally, I immediately ignore marriage candidates that would produce slightly inbred children if the marriage I am arranging is in any way connected to my own line of succession. My firstborn son, and his two younger brothers, get nothing but completely unrelated foreigner women to marry. I sometimes get a bit lazier when arranging other marriages, depending on circumstance.
If you did the same with third cousins (the least related character which will show as a relation) then your maximum CAs would be 16 meaning, at most, doing it 4 generations in a row, you'd get an 11% chance of inbreeding.
This also doesn't account for the pure blooded trait or the level 3 blood legacy which allow you to pretty much marry first cousins and not worry about it too much. Sure, you get the occasional dwarf but who doesn't love Tyrion Lannister. Gives some variety to the herculean, beautiful geniuses.
EDIT: Funnily enough, I've actually had the opposite problem in my quest to have an inbred child (for the achievement). The RNG gods have not smiled on me, in spite of deliberately inbreeding siblings for multiple generations. I've had multiple inbred relatives but never one who was actually the child of my character at the time.
And quite frankly there is no other way to maintain the top tier congenital traits, because the AI never considers those. So after the initial wave of pre-made NPCs is dead, they are pretty much extinct.
For example the chance for the Genius trait to appear at birth or on random generated NPCs is only 0.05%, and for the lowest tier (Quick) it also is not more than 0.5%.
Ergo only one out of 200 female courtiers is Quick, and finding this one at the right age range, and also with somewhat useful skills and no terrible personality is practically zero.
If that courtier is also related to some landed character, you'll have a random alliance, and you already know that you will be called to war every 2 minutes for the rest of your life.
Bottom line: Those female relatives are the best wives, no matter how silly / unrealistic Paradox has designed the inbreeding rules. Getting your daughters married matrilinearily with random lowborns also makes sure there is a decent pool of candidates to choose from. These lowborns don't necessarily need congenital traits themselves, something like high Learning or Prowess makes them perfectly useful at court either way.
TBH if you worry so much about a low chance of inbred heirs, you probably shouldn't play the game at all. The chances of having your monarch or his heir assassinated, die in an accident, in battle or from disease are many times higher.
And even if there is an heir who is dwarf or scaly or inbred, you can either disinherit him (that's what the tool is for) or, with max crown authority, designate another son as heir.
If you willing to futz with the rules a bit; set diplomatic range to restricted and play in Iceland. Also set the world to be predominantly asexual. Reduces the cuckoldry enough that you can get the achievement that way.
I was not going to hunt that one in regular settings. TOO many cooks in the pot, as it were.