How to access API with Password authentication disabled?

I’m trying to post with the WriteFreely iOS-app, but can’t get it to work, as it results in the error:

The operation couldn't be completed.
(WriteFreely.WFError error 403.)

I’m also trying to use a home-made action in Drafts, which results in the following error:

"code":403,"error_msg":"Password authentication is disabled."

Other than enabling password authentication, is there a way to make the API functional?