Fields that support languages cannot be edited in ProcessProfile if 'page-edit' permission not granted.

[kixe]

If a field has been added to the user template and marked as editable via ProcessProfile, it should be editable if the user has profile-edit permission.

However, for language-supporting fields, this only applies if the user also has page-edit permission, otherwise, entries will not be saved and the following message will appear in the field for any language:

"Changes to this field will not be saved because you do not have permission for language xy"

The page-edit permission should not be a requirement to edit fields via ProcessProfile.