The risk of blood clots from hormonal birth control is a bit more than 1 in 2000. The risk of blood clots from the J&J vaccine assuming this new blood clot adverse event is causally linked to the vaccine is about 1 in one million. In other words, it’s basically a rounding error on the blood-clot-risk scale regardless of whether you’re already taking hormonal birth control.
And of course the risk of blood clots from getting covid-19 is itself quite significant–possibly as high as one in five. Even if it were just one in one hundred, and you were only 1% likely to get covid, and the J&J vaccine causes blood clots, the vaccine still lowers your overall risk of blood clots quite significantly.
