Submission of a form on wordpress OK with chrome but not valid with Firefox, Safary
Its down to permission, make sure anonymous user can access the profile. It is possible that on chrome you are logged and safari you accessing the profile as anonymous user.


Navigate to CiviCRM >> Administer >> Users and Permissions >> Permissions (Access Control). Click on 'Wordpress Access Control' link. 
Look for 'CiviCRM: profile create' and check the box under anonymous or authenticated role column and save the form.