The following answer was my original answer but it is wrong and does not answer OP’s question:
Simpler solution, no CSS hack and no editing Django codebase:
Add this to your Inline class:
(this is only applicable to inline forms, not foreign key fields as OP asked)
The above answer is only useful to hide the “add related” button for inline forms, and not foreign keys as requested.
When I wrote the answer, IIRC the accepted answer hid both, which is why I got confused.
The following seems to provide a solution (though hiding using CSS seems the most feasible thing to do, especially if the “add another” buttons of FKs are in inline forms):
Django 1.7 removing Add button from inline form