Can you be a feminist and pro-free market at the same time?

The assumption that you cannot usually rests on a conflation worth unpacking. It mixes up two different things: existing markets, shaped by centuries of discriminatory law, unequal property rights, and exclusionary practice, and the idea of genuinely open markets, in which every individual can participate on equal terms. Much of what critics correctly identify as harmful about capitalism is, on closer inspection, a critique of the ways markets are not open. Women excluded from certain jobs by law. Paid less because regulation crowds them into a narrow range of roles. Unable to own property independently in practice despite holding the right on paper. These are not the outcomes of free markets. They are the outcomes of markets that were never free to begin with.

Consider what a genuinely competitive labour market does. Employers compete for workers. A firm that refuses to hire capable people based on sex, caste, or any characteristic unrelated to ability hands its competitors an advantage. Over time, that pressure is one of the most powerful forces for breaking down exclusion, not because employers become virtuous, but because they respond to incentives. The historical examples bear this out. When labour shortages forced employers to hire women into skilled industrial roles, women excelled, and the justifications for their exclusion quietly collapsed under the weight of evidence.

The feminist project, in its economic dimension, is to remove the barriers that prevent women from participating on equal terms. The free market project is to ensure that markets are actually open to everyone. These are not competing demands. They are the same demand made from different starting points.

The tension people sense between feminism and free markets is real, but it is a tension between the ideal of open participation and the distorted reality of markets still shaped by law, habit, and accumulated exclusion. Resolving that tension does not require choosing between the two. It requires removing the distortions that make them appear to conflict.

So yes, you can be a feminist and pro-free market at the same time. In the economic domain, if your feminism is about individuals rather than groups, and your market liberalism is about genuine openness rather than defending existing arrangements, you are largely arguing for the same thing.