If you DID want to make it a plot point, there are almost infinite number of ways to do it.
-One of the other characters is maybe a dead ringer for a known pornographer. You could make this an ongoing thing where he's constantly confused for a smut peddler.
-You might simply have an over-zealous or Corrupt sheriff; he isn't allowed to just arrest any woman for crossing state lines, but he either doesn't know or doesn't care (or does know, but wants a payoff)
-There might just be a local ordinance forbidding unwed women from out of state being in the town; the ordinance won't survive a challenge in any higher courts and will be nullified in 6 months, but that doesn't help the characters NOW as they sit in jail for violating it.
Uhoh, that sounds dangerously close to being
creative there goatman, maybe dial it back a bit and return to the grey sludge that occupies most modern TTRPG experiences, thank you kindly.
I've been reading CoC stuff lately and I'm really impressed with the amount of historical verisimilitude they're going for. The Horror on the Orient express books are just chocked full of references, further reading material, diagrams, explanations (the goddamn book is recommending me read historical travel guides on Istanbul for God's sake that's wild) - it's borderline edutainment, very nice. I think D&D can really benefit from this as well but the problem is that you have to be a different type of nerd autist to read up on the world and the dieties and backgrounds and factions etc. all that boring shit versus "go here, stand still, fight that, next room please".
And you know what, there's a time and a place for brain off, basic shit, I get it, not trying to be a dick and requiring a textbook for frontloading your dungeon crawl.
But how many DMs are gonna read a bunch of supplemental material from 20-30 years ago to help run Ravenloft settings? How many are sitting there scumming wikis that have been purged and re-purged throughout the years thanks to troons and dangerhairs bitching about racism or bikini-armour? Like everyone says, it's a game it's meant to be fun, and the DM/GM is included in that so you just have everyone's idea of fun is aligned (and for my groups I am quite fortunate that that is almost always the case).
But I think you can bullshit away a lot in a pure fantasy setting versus something like the 1920s because I think the threshold for including BMW 5 series with optional heated seating is higher than you'd think and anachronisms/inconsistencies are tougher to mAgiCk away.