Though if you really wanted, you could provide contraception without providing abortion services (it's a policy that these two are often combined, not logistical or economic or any other necessity.)

You have to avoid ever mentioning abortion as an option, not just avoid providing them yourselves. There are tons of places that only offer contraception which are affected by this rule. There are organisations which don't even offer medical services but which support the availability of abortion, and they also lose funding under this rule.