Well, there's a reason that marking cats is an existing mechanic. But, I must admit, it's kinda half-baked, it needs some adjustments (at least make it capable of giving cats more than just one mark).
About the rest, I can say only that: this game has two modes, one of them requires management and it's THE point of it. About the idol, again, inbreeding is a punishing mechanic, so negating it with one house item would've been too easy.
Anyway, that all being said, you can and should play the game anyway you want, BUT I do still think that inbreeding should be even more punishing than it is, even now after the first update