It's nothing egregious, but as someone who actively gets annoyed by incest tropes, it's definitely noticeable.
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Like that last sentence is reasonable in a vacuum, but no one in avns actually talks like that. A hallmark of incest games is the need to CONSTANTLY reference the relationship, as opposed to normal interactions where you'd hear "Hey John wassup?" or "Hey how are YOU doing?" The variety common here is "And how is my [variableRel] doing?" I'm probably asking too much, but I'd love for a game to have a relationship variable set where the player would have no idea where the design motivations lay.
Slutty suggests promiscuous or provocative, and from websters, generally in a way that shows bad taste.
To me, skanky is similar, but it carries more of a "cheap" or "sleazy" connotation, they not only appear promiscuous, it's in a tawdry or low class way.