Unless the sentence is addressing men who speak in conventional ways, it is missing a comma.
With no comma, conventionally speaking appears to modify "men" (albeit in an awkward, non-idiomatic way.)
Conventionally speaking men are more likely to be hired as broadcasters than those with effeminate voices.
When a comma is included, "Conventionally speaking" qualifies the entire statement that follows.
Conventionally speaking, men are more likely to be hired as broadcasters than women.
Also - ruakh correctly points out that here "while" is being used to mean "whereas", rather than "at the same time as." Formal grammar would put a comma in front of it:
Conventionally speaking, men are supposed to earn, while women are supposed to sit at home, do housework and discipline the children.
If the author meant to say that men should be earning at exactly the same time as women do chores, the comma and the "are supposed to" could be removed.
Conventionally speaking, men are supposed to earn while women sit at home, do housework and discipline the children.
1 is definitely wrong, and
2 is formally incorrect also.