The background feature for folk hero states that you automatically find shelter, etc.. Why? You ride into town with 3-5 other individuals, no one knows you, you just walk up to the door of the nearest commoner and say "Hello fellow commoner, we are being hunted by the sheriff, please hide us"? That's ludicrous.
Whether it's ludicrous or not depends on what happens next. There's nothing inherently ludicrous about travelers seeking shelter at a nearby dwelling or common folk protecting one another from an unjust authority. Rustic Hospitality says, "You can find a place to hide, rest, or recuperate among other commoners," so I assume in your example "the door of the nearest commoner" has been identified by the folk hero as a good place to hide after looking around for such a place. Now, whether the person who comes to the door agrees to hide the folk hero depends on whether the folk hero can overcome any natural suspicion of strangers they might have. Luckily, their feature states, "you fit in among them with ease", so it can be assumed the folk hero's mannerisms, way of speaking, and general demeanor transmits to other commoners a sense of trustworthiness and belonging, so the person at the door agrees to hide the folk hero. Whether they agree to hide the rest of the party is another matter because the feature doesn't cover that. I think it's a good beginning to a social encounter. The commoner agrees to hide the folk hero but isn't sure about the other party members, and it's up to the party to convince them to take the risk to help.
There is no reason to have any kind of instant connection unless you spend time with the people and live with them for a while.
Who's to say time isn't spent at the door establishing such a (non-instant) connection. It isn't ludicrous unless you make it ludicrous.
The sailor background feature states "You might sail on the ship you served on, or another ship you have good relations with (perhaps one captained by a former crewmate)." It literally states in the background feature that you know someone. Which does not always make sense.
I mean, sure, it states that
perhaps a former crew mate captains the ship on which you secure passage. So you
might know someone, but if for some reason it doesn't make sense for you to know anyone, there are other options, so I'm not sure why you're focusing on knowing someone. More important to the feature is your connection to the ship on which you gain passage. It could be someone you know, or it could be something else that makes sense in the established fiction.
Again, the background feature states that wherever you are you can find someone to send a message. How is that supposed to work? Find someone with gang tattoos and say "Hello fellow gang member, please pass this message." Why would they? What possible motivation would they have, much less why would they have any contact outside of their local city or even district?
It would be like me going up to a fellow gamer at a convention and since we're both gamers asking them to pass on a message to someone I know that lives halfway around the world and expecting the message to magically get there. It's like playing six degrees to Kevin Bacon and expecting to be able to get a message to Mr Bacon by telling someone you know who might know someone who might know someone [repeat to get to 6 times].
Well, no, it wouldn't because you and your fellow gamer (afaik) are not part of an underground criminal network. The "local messengers, corrupt caravan masters, and seedy sailors who can deliver messages for you" are part of such a network. They might be identifiable to the criminal because of the tattoos they wear or any number of such things. They're motivated by their involvement in organized crime. It's their job. The network extends beyond their local city or district.
We take different approaches to the game. In world logic and cohesiveness matters to me more than it does to you.
This is complete and utter nonsense. Players being able to make stipulations about the fiction as part of the action declarations they make for their characters doesn't make a game any less logical or cohesive than yours.
Because you don't accept that the logical inconsistencies required matter to anyone else because it doesn't matter to you. I have no issue with you running your game differently, it's your insistence that anyone who doesn't agree with you is playing the game wrong.
I don't accept logical inconsistencies
are required because I do this without logical inconsistencies. The only people who keep saying they're required don't seem to have much experience using background features to begin with.