The ideology of male breadwinner is quite alive in more conservative and evangelical circles. Man living in such social group whose women earn more have lover social standing and consequently don't want it. Then there are people who don't care and I know of no groups that would believe in women being expected to he breadwinners.
Ideology of independent working woman seems far more pronounced to me. We all are expected to work, which necessarily makes having children – especially early in life, when they have the highest chance to be healthy – a big bother for women, and feminism doesn't help here in the least, even if it slightly compensates for the issue of "ideology of male breadwinner".
"Ideology of independent working woman" is basically ideology of same expectation on men and women. It does not compensate anything, bias in who is expected to earn more goes other way. A single women does not need to earn more then non-existent husband to feel enough feminine.
So the bias would be toward that way.