This is part of the problem with this topic: neither side talks honestly about the effect, and both sides collapse the nuances down to easily defeated straw men.
The "wage gap" has never been attributed, by any study, soley to the impacts of discrimination for equal work – though some effect is seen. For instance, the 2009 Bertrand showed that there was a 10% gap between new business school graduates, based on gender [0]. That difference never really disappears, on average, across the population [3].
However, the effect definitively widens at child birth, with women shouldering an unequal amount of caregiving responsibilities [1]. Whether married or unmarried, women with children take a hit. However, when married, even with children, men don't take a hit. Married men generally earn more than unmarried men. In fact, they generally earn more than everyone else – though this effect is shrinking. [2] Unmarried women, without children, will generally earn 90% of an unmarried, child-less male assuming equal education levels. We see a growing disparity, with unmarried, childless women overtaking unmarried, childless men in earnings due to the education gap. Eliminate educational differences, and the gap reappears.
When either side collapses the "wage gap" down to simplistic tropes like individualized gender-specific discrimination or "choices", they're generally signaling they haven't studied the topic beyond reading a few headlines.
It's way more complicated, and interesting.
[0]: https://scholar.harvard.edu/files/goldin/files/dynamics_of_t...
[1]: https://www.henrikkleven.com/uploads/3/7/3/1/37310663/kleven...
[2]: https://research.stlouisfed.org/publications/economic-synops...
[3]: https://docs.iza.org/dp9656.pdf