Yes, as a non medical/statistician person, I'd be really surprised if we had the same quality and quantity of data on the birth pills and this new vaccination.
The risks could be higher, but maybe our data is not yet there.
Just as a side note, the risks (and gains) are different, maybe I really don't want a child accidentally, but I don't consider the coronavirus too dangerous to me (it's just a hypothetical, this hypothetical person could be wrong, but in the end we all operate on incomplete data)