I just looked up the law on the UN website.
Grounds on which abortion is permitted:
To save the life of the woman Yes
To preserve physical health Yes
To preserve mental health Yes
Rape or incest Yes
Foetal impairment Yes
Economic or social reasons Yes
Available on request Yes
HereBut either way, the US also has abortion legal, though I wouldn't consider it a socially conservative state, but rather a nation with a lot of social conservatives. A socially conservative state are nations like El Salvador and Honduras.