No, they don't. It's called pro choice for a reason. I will agree that contraception is priority number one, as will the doctors most likely. Abortion should be a last resort option. And it's the vooman's body, so it's up to the vooman to decide whether or not she wants to abort.
And no, China Virus vaccines aren't remotely the same. It's apples an oranges. Unvaccinated people can spread more viruses than vaccinated ones. If a vooman aborts it doesn't make other voomans nearby magically abort.
Then there's also the issue of hospitalization rates. Hospitals were being overcrowded with china virus patients even with all the restrictions. At some point they would've eventually just be so crowded that death rates would go up because of the reduced quality of care.
Vaccines significantly reduced hospitalization rates and the severity in general. Now, that also means that rushing with vaccines that didn't even reach phase 3, like China and Russia did, isn't a good idea. But now we do have proper vaccines.