It is an interesting question to what degree Yidden were learned. Of course, it changed over time and country. Difference between Vilna in 17th century and Morocco 10th century might be more than between Lakewood and Tom’s River.
Stam, a lot of gemoras discuss various behaviors of population that are not very learned. Say, making nedorim left & right seemed to be quite popular. It seems that classicial amei haaretz were at least “culturally Jewish” – we presume that they did maaser but not sure that they did. To appreciate that – would you say about a Reformer or a socialist – you presume they keep kosher but just in case, I won’t eat there? unfortunately, not …
I think one presumption is that Am H. knows Tanach (without Rashi) but not Mishna. Thus, you should admonish people if your words have a clear support in a posuk (not just a hint0 and, presumably, they’ll listen.
You can probably get a better picture if you go through Gemora cases where Rabbis make a takanah based on what majority of people will do or accept.