I think you have to differentiate two elements of the debate.
Rugby Union fans tend to be from better off backgrounds, this is particularly noticeable if you are anywhere near Twickenham on an international match.
I dont believe that the players all come from the same background, rugby is played more in public schools than football, Equally people take up rowing or polo and these are definitely elitist.
In the state schools I went to in the midlands or south west, we played rugby in mid winter. To be fair it was a good excuse to stay warm when we got the ball in the scrum, nobody let it out for a good few minutes. It usually took someone to break wind before the scrum collapsed, and a fight started. We also played football and cricket.
Just because Rugby Union is bigger in the Midlands, South and South West doesnt mean that it is posh. Equally Rugby League is played in the North doesnt just mean it is played by more down to earth people. There are many normal people based here in the South West. The big divide is if you are good at sports you would want to go into football, there is more money, less injuries and it is possible to try to play in multiple positions. Rugby injuries are common, teams are smaller and you tend not to be able to move positions, if you are built like a brick s**t house you are a forward.