Add a field to the bottom of the form called Current User with the default value set to the current user token. This field will get auto-populated with the current user's username when the form is opened. 

Next, go to the field rules page. 

Set up a field rule saying Hide Fields A, B and C, if Current User is User A. You can add more conditions to the same rule using the When Any condition. If you say When Any is true: if Current User is User A, if Current User is User B... this will allow you to use the same rule to hide the fields for multiple users. Or you can set up a specific rule for each user. In this case, since the fields are hidden and you don't want the data, you can set these to Ignore values when hidden. 

If you want to hide this Current User field from the form, you can create another field rule to Hide the Current User field Always. This will make the field not show up, but still work for the above field rule. In this case, you want to Save the data of the hidden field, because even though it's hidden on the form, you want that value to be used in the other field rules.