You ride into town wearing armor and/o carrying gear that's worth more than the total GDP of the village. You're with up 5 other individuals. Combined, your group has more wealth than anyone has dreamed of.I don't think they're as narrow as you present them.
The Folk Hero says you have a destiny. You're marked for greater things. 'Already the people of your home village regard you as their champion, and your destiny calls you to stand against the tyrants and monsters that threaten the common folk everywhere'. (Note the use of 'already' rather than 'only'.)
The ability itself says 'Since you come from the ranks of the common folk, you fit in among them with ease. You can find a place to hide, rest, or recuperate among other commoners, unless you have shown yourself to be a danger to them'.
The clear implication is that the character has some quality of 'folk hero-ness' that commoners recognise and respond to regardless of whether they know them or have heard of their specific exploits. It's like having a very narrow kind of 18 Charisma, in the appropriate environment you just sort of speak the right alignment language and people take to you.
I find it difficult to believe that you will automatically and instantly be accepted. But take it a step further. You don't look or have the same customs as the locals because you're halfway around the world. Maybe you're a dwarf and this is a goblin village, the war of Dwarven aggressors is still fresh in their memory.
I don't have a problem with being able to relate and possibly gaining advantage on checks. It's the automatic guaranteed "You can find a place to hide, rest, or recuperate among other commoners, unless you have shown yourself to be a danger to them."