Emma invites Martin to Hartfiled out of courtesy, becuase he's about to marry her protgee. She's showing kindness and condescension, just as Mr K does at times but that is a long way IMO from "being willing to mix with people of less than strict gentility"..
Sorry but while the Coles are now "risen" to a point where they can expect to dine iwht the local first families, the Martins aren't. They are not rich enough, even if they live comfortably and have a summer house...
I dont see that a yeoman farmer even if doign well, is going to have enough mony to live in a style that would mean he coudl comfortably associate with teh Knightleys... but he would probalby be invited occasionally as I've said....gthe Knightleys woudl problaby stand as godparents to his children, tehy woudl be there to consult and advise.. that's how the patronage system worked...