I had no idea such a gag rule existed. Does this affect distribution of contraceptives in some twisted way as well?

It affects the distribution of contraceptives very directly. It means that no organisation that ever talks about abortion as an option for women can receive American funding. Doesn't matter if their primary work is providing contraception or providing childcare, if you tell women they could get an abortion, or you lobby a politician to make abortion more available/safer, you lose funding. https://www.globalfundforwomen.org/mexico-city-policy-global...

Of course it does. Many organization that provide contraception also provide abortion services, and therefore are ineligible for funding.

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.