This is nonsense because it doesn't seem to control for age, education, income, or (most importantly!) whether a woman was trying to get pregnant.

Even before Covid, it has been well established that women are less likely to become pregnant if they're higher income, higher education, etc. Those are the same predictors of being vaccinated.

If you read the conclusion the authors point this out and address it. They argue against reaching a causal conclusion but given the magnitude of difference ask for more study.

Your approach argues for outright dismissal without any analysis or alignment with other factors.