Does status difference matter in interpersonal relationships today?

Would a woman having a lower status than a man create problems in relationships? For example, a woman working as a laborer and a man as an engineer. What if the woman doesn't have a family? Would the man respect her in such a situation, or what should the woman do to earn his respect, even if she had to drop out of school due to lack of money?

Does status difference matter in interpersonal relationships today?
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