I think you're being too reductionist. They don't defer to authority, they are looking for a provider. Notice, I didn't say "when the husband was conservative". It was "married at all".

When women are married, man = provider. This necessitates strong masculine values and policies that would promote an individual man's success. Which aligns with many conservative, or even libertarian values. When the woman is unmarried, provider = state/society. This necessitates a strong governmental protection racket which preferentially treats women generally, in the hopes that some specific women (the women voters) will benefit.