We fixed the problem by changing the setting 'ARITHABORT'.
The wrost thing to try to find the problem was that the stored procedure call that didn't work from entity framework, worked from SSMS and that was because SSMS overrides some of the options and we didn't see that problem.
We installed the old application into the same environment (same DB) and at some other different place of the app, it showed this error:
UPDATE failed because the following SET options have incorrect settings: 'ARITHABORT'. Verify that SET options are correct for use with indexed views and/or indexes on computed columns and/or filtered indexes and/or query notifications and/or XML data type methods and/or spatial index operations.
So the problem was with an update, but that update didn't come directly from the SP but from a trigger triggered by a trigger triggered by the SP, so we didn't have any log of that, as crazy as it sounds.
Luckily for us the old app we try to replace "fixed" the problem by hinting us into the right direction.
Thanks everyone for your help!