I AM THINKING TODAY ABOUT MAX AND STAR. How he sees her, and what he thinks about her place in his happy little white picket fence all-american vampire brady bunch family.
(shout out @aberfaeth who got me chewing on these ideas like a bone)
Some options, pretty much all of them insulting to Star and reflecting a very reductive understanding of her as a person which I do unfortunately believe is in character for Max, and all of them absolutely steeped in misogynoir:
Does not know her deal, doesn't think too hard about it. Unlikely, sure, he's at the gigs and everything. But maybe he's just like. Well, David can have his fun with these little boardwalk girls. And doesn't question it. Boys will be boys, ah ha ha ha jovial wink, nudge, etc.*
Knows that she's a half-vampire, but isn't that concerned about it. Max only really thinks about others inasmuch as they serve his goals (thinking a LOT about @pillbuggery's excellent Pete and Max meta), and Star does not really come into that. She's not in his way, and she's not immediately of use to him. Therefore, she's of no importance to him as either an obstacle or an asset. Immediately forgettable for the time being.*
Won't take action against her now, because of the above, and also because here is some evidence of David's interest in a woman. Which is probably very, very important for Max to preserve for his own mental understanding of David and their family. And probably to use as a cudgel against David's expression of any queer desires, as well as any queer identities in his house. (joke's on him in many regards here, as relates to David, Star, the other boys, pretty much everyone. Whole house queer identities).
Potentially he sees Star as the "female influence" that he's trying to instill in the boys himself through Lucy. So until he gets Lucy on board, Star makes for an acceptable substitute to keep the boys from establishing too rigid of a homosocial unit (and perhaps he reads her influence as checking their more murderous rampages), until Max can get his own chosen candidate in the role. At which point, Star is in very immediate danger.
Alternatively: Star will absolutely be safe in Max's happy vision of the family future. Because Max, above all else we know about him, is THEE master manipulator. And he IS at the gigs. And he KNOWS David. So he knows a valuable asset when he sees one. David, who lets no one in and has a survivor's gift for creating his own impermeable armor, has tripped up and exposed one weak point. When Max has the chance, he plans to exploit the fuck out of that weak point, in any way he can, as another leverage point for keeping David under his control. So he can allow things to unfold as they will without worrying about it much right now, secure in his certainty that when the time comes he can make the most of it.*
