Should other countries provide asylum for women fleeing American oppression?

As we've all seen on the news religious fanatics are about to make abortion illegal in the USA. Victims of rape, including incest will be forced to bear their attackers child. It's obvious many will flee to safe countries perhaps even before anyone knows they're pregnant to get an abortion.
Many countries have a record of helping people fleeing persecution from restrictive oppressive regimes. So does the rest of the world have a moral obligation to provide sanctuary to American women seeking abortion?
Should other countries provide asylum for women fleeing American oppression?
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