I recall a study published in Lancet many years ago that stated 1 in 10 women who had abortions became sterile as a result of the abortion procedure
Which means 90% didn't.
I don't put much faith in studies claiming that abortion causes sterility. Not to mention that with IVF, the type of infertility that could be caused by an abortion or other gynecological surgery, namely tubes blocked by scarring from infection or trauma, is no longer an obstacle to having babies -- just can't make them the natural way, which in the case of women who are prone to getting pregnant when they don't want to be, isn't necessarily a bad thing.
But the history of abortion-as-contraception in the Soviet Union, which had a pretty primitive medical system, suggests the claim is bunk anyway. Various studies found that during the 1970s the AVERAGE Russian woman had had somewhere between 9 and 11 abortions. If one abortion, under normal Western medical standards could make 10% of women infertile, there's no way that most women in a large population could still be getting pregnant after 8 or 9 Soviet clinic abortions.
The Lancet often covers topics on a global or regional basis, however. In 3rd world countries, where medical facilities practice virtually no infection-control measures, and most patients don't have access to antibiotics after any procedure, I wouldn't be surprised if natural fertility was lost in well over 10% of women having abortions there. But given that many women don't survive childbirth there, that wouldn't be much of deterrent. In addition, any place where abortion is illegal is likely to have a high rate of abortions performed in non-sterile makeshift facilities, with the patient not getting a prescription for antibiotics afterward. It's very easy to get blocked-tube infertility from any kind of gynecological infection, including those that are not sexually transmitted.