because many female contraception methods involve medical procedures and require medical management just like other medical procedures. a hospital doctor should be able to prescribe a series of doses of estradiol and progestin if the patient requests it and the doctor agrees it will have the desired effect.
generally, contraception is cheaper than unwanted pregnancies. so economically-speaking, it makes sense.
but if a woman decides she is ready to rumble and wants that baby - good idea to work with the obgyn you have been working with all along.
gynecology covers a lot of health issues, from contraception to STDs. it's kinda artificial to ring-fence one procedure because a virgin (or child-molesting) bishop doesn't like it.
generally-speaking, you also want your gynecologists to be available in a hospital. in particular if you live in a community served by only one hospital.
maybe you also live in a community that doesn't support a separate clinic. in a catholic town, you may find the economics doesn't work for a minority of non-catholic women. so then a hospital is your only recourse.
i can see no reason for religious intervention in female contraception medicine any more than there ought to be religious intervention in vaccination decisions.
and in my view, there's no reason for the government to permit discrimination against women's health and fertility issues by interfering religious groups.
religious people should not be circumscribing a woman's personal choices via funding and policy setting.
you want to fund medicine, fund medicine. let the doctors perform their services unhindered.