It is OK as long as you have an exit plan/alternative. If you know you can roll your own or switch to one of a number of providers in a week or so and that is a known risk you an can manage it.

Depending on what data you are trusting the APIs with there is also the security risk. CirleCI have just suffered from MongoHQ's security failure in a way that is extremely urgent and customer affecting.

so true, your core business should not rely on a third party API that doesnt have any contractual obligation with you.

Yet APIs can be a great way to launch a product fast. You have to become independent as soon as you can.