I have a use case where some Apex code will need to run as a user with this profile. I am updating some fields in this code and then performing an
update on the contact that's associated with this user. However, the DML update throws the following error.
System.DmlException: Update failed. First exception on row 0 with id 0030t00000mAa8oAAC; first error: INSUFFICIENT_ACCESS_ON_CROSS_REFERENCE_ENTITY, insufficient access rights on cross-reference id: 
I'm assuming this is because the user this is running as does not have the proper permissions. I've given them read/write access to this field via field-level security and when I go to the sharing settings for this profile it shows read, write, and edit access to the contact object, so I'm not sure where to go from here.