Processing shall be lawful only if and to the extent that at least one of the following applies:
b) processing is necessary for the performance of a contract to which the data subject is party or in order to take steps at the request of the data subject prior to entering into a contract;
This legal basis is a lot more clear and a lot less stringent than point f) legitimate interest as it does not explicitly require you to establish "legitimacy" and balance it against vague "interests or fundamental rights and freedoms of the data subject".
f) processing is necessary for the purposes of the legitimate interests pursued by the controller or by a third party, except where such interests are overridden by the interests or fundamental rights and freedoms of the data subject which require protection of personal data, in particular where the data subject is a child.
Would the same argument apply to using Strip or Paypal to accept credit card payments? The site could deal directly with a lower level payment processor which would reduce the number of third party entities that see the user's credit card.