Faolyn
(she/her)
What I would do is, if the player said "I want to find a ship to sail on and use my background to help me do so," I'd say something like, "how are you doing this?" Then one of the following may occur:It seems that it's possible that one of the reasons that the background feature is being objected to is the idea that the player will just make up a contact (or a ship) on the fly and then force it into the DM's established setting.
There are DMs and tables that allow that sort of thing (and in which case, those DMs don't usually establish the details of the setting beyond a loose framework) but it's far from the usual way that D&D is played. I don't think @Faolyn or @Hriston was ever advocating for this sort of play.
One: The player may then say they're going up to the captain or first mate and trying to use their nautical knowledge to sound impressive. That's a Persuasion check. (Someone who does not have the sailor background or at least proficiency in sea vessels would have a higher DC and/or obviously wouldn't be able to use their proficiency bonus, or may have to roll Deception vs. Insight with a bonus for the captain).
Two: The player may tell me that their cousin Two-Eyed Bob the Sailor once manned a ship that docked in this port often. There would the above-mentioned Persuasion rolls, but with an added wrinkle of me getting to decide how the ship's crew felt about Two-Eyed Bob (colored by whatever they've previously said about this cousin--and if this is a brand-new cousin they just invented, then I get to decide[1]). I might roll a die and decide whether they liked him based on the result (like, the higher the number, the more they liked him). In which case, there's a chance of backfire. I would allow this for non-sailors as well, but probably with penalties to the roll.
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[1] This also depends on how out-of-character Two-Eyed Bob is. If the PC had said they come from a line of sailors and pirates, then OK. Two-Eyed Bob is plausible. If they had said they had run away from the farm their family had been working for generations to become a sailor, I'd say, "yeah, no, that's totally contradictory to everything else you've said. However, I can't imagine any of my players actually trying to pull this. Everyone at my table is a reasonable person.
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Three: The player may tell me that they worked on a particular ship that docked here. In which case, we have a conversation about the ship and why they left it. This may involve them inventing some details (probably in the form of noodle incidents) that had previously never come up.
If they had previously established that they only sailed on the Inner Sea and they were currently on the coast of the South Sea, then we'd have to have some discussion about how that boat got from the Inner Sea and the South Sea. It's entirely possible that we'd then establish a new fact about the world (a connecting river, a canal, something else). It's also possible that the player would realize there was no way the ship could have moved seas (see above re: reasonable players).
IME, these sorts of conversations take maybe 5 minutes or so, 10 max, which is not an unreasonable amount of time and is certainly far less time than we had to pause the game yesterday when it was interrupted by Toddler Surprise Attack (did you know that if you put your hands over your ears, it works just like daddy's headphones and you can hear what all the other players are saying?)
Four: If I felt like it, I could just have the ship they used to work on, right there in dock. How did it get there? Good question! Want to get on and find out?