I think it's very important that we all understand that conflict and morality are separate things. Instead of using my own words to describe the two things I will use the reliable Oxford Dictionary (.com).
Morality - "Principles concerning the distinction between right and wrong or good and bad behaviour."
Conflict (as relevant to narrative) "A serious incompatibility between two or more opinions, principles, or interests."
Notice that both definitions use the word "Principles". That is because conflict within a story can absolute be about morality or be centred around some kind of moral or immoral act. That does not mean that conflict and morality are synonymous with one another. It is not true to say that every conflict is related to morals.
Morality is about what is right a what is wrong but I can think of hundreds of possible conflicts which have nothing to do with morality. Here's five just off the top of my head:
Cassidy wants to climb to the top of the last mountain that her adventurous brother never got to climb because he's dead or whatever but she can't because she's in a wheelchair. Goal = Summit mountain Conflict = Being in a wheelchair makes climbing up stairs difficult let alone a mountain.
Jimbob has always wanted to make his own movie and he's finally got his creative team together to do it but the project is going to cost them 100,000 monies and they only have 10,000 monies
Sarah has a big crush on her roommate Katie. When Katie goes on holiday she asks Sarah to look after her dog. Sarah wants to impress Katie and get in her good books but she has a fear of doggies. Oh no!
Glimnork the alien wants to visit earth in disguise in order to discover what all the fuss is about with this whole "Big Mac" at McDonald's but he has severe social anxiety that disrupts his cloaking device (because it's linked to his brain or something). How will he hide his alien identity from the humans? Will he ever get a chance to chomp into his tasty Big Mac?
Freddy Five-fingers Mcgee lost his house in a freak fire (he was too drunk to remember how it happened) out in the Wild West and now he needs the money to rebuild. He used to be amazing at poker but now -- despite his name-- he ain't got no fangers left. How will he play? And with his drinking problem, will he be sober enough to win?
All of these ideas share three things in common:
- They all have a goal and a conflict
- They are all Academy Award winning ideas (lol)
- None of them directly deal with morality.
Why? Because morality and conflict are not synonymous and because stories are not inherently about morality. Or to put in another way morality is not an intrinsic part of storytelling. Just because you have conflict that does not mean you are automatically going to be dealing with what is right or wrong. So again, to say specifically that "Every story is a morality play" is, in my view, false. There are plenty of stories which are not "morality plays" and don't focus on morality or use it as a theme.