I would say 1) Only men could act, not 2) Only men could play. But is number 2) OK? I would choose 1) because there is no object. What would a native speaker do? and Why?
Both 1) and 2) lacks a direct object, Ripley. "play" functions as a base verb, a non-finite verb. It's an infinitive, like 'to play'. With modals, like "can", the second verb doesn't carry tense.
Only men performed on stage.
"could act" is ambiguous. It also means, had the ability, or woman also performed roles, but they couldn't act (i.e., they were bad actors). I think the meaning you're after is permission: only men were permitted on stage.