By default Customer Community Login User profile is quit limited and this is fine, because the main Salesforce vision from the architecture perspective do not for see to allow this user to do much.
Although from the practical perspective, there might be some use cases, for example, when Company ABC decided to use Formyoula forms to allow their community users to collect data offline and push into their Salesforce as a new Leads without even having an access to Leads object in Salesforce.
To be able to use Formyola with their Salesforce, they need to have "API Enabled", but by default it is not available.
The hack is to clone standard Customer Community Login User profile.
And now you are able to enable API for the user.
I hope this small hack/trick was helpful.
Please let me know what was your use case in the comments below.