1) Women seeking abortions do not go to Catholic hospitals to get one.
2) Catholic hospitals should not be getting government funds.
If they are being compelled to provide care to those who cannot afford such by the State and Federal Gov, then yes, they should be getting government funding. However, there should be no compunction to perform medical procedures that violate their charter.
Some,women would go to a catholic hospital for an abortion.
They are those that want to file a lawsuit against the hospital.
Who goes to a chinese restaurant and sues the place because they wont make them lasagna? Someone who wants to file a lawsuit against them.