"Wasn't done" means "didn't happen" but it does not necessarily mean that it was socially acceptable.
Why not just say "wasn't socially acceptable in the past"?
"A common-law marriage wasn't done in the past." Is it OK to say this to mean that a common-law marriage was not socially acceptable in the past?
As Raymott said "... is not the done thing" is the usual style. You might hear "It's just not done" too but context would dictate whether that meant "socially unacceptable" or simply "it doesn't happen".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
It's factually incorrect. Common-law marriage was very common in the past in peasant communities.
I just wanted to figure out if this definition of 'done' from the Merriam-Webster Learner's Dictionary is accurate.
"3 : socially acceptable or fashionable Getting a divorce just wasn't done at the time."
As is evidenced above, it's not.