Does the script have the option checked to "Run script with full access privileges"?
those fields have already been set not to allow access in Browse
Do you mean you have removed field entry in the Inspector? That's not a security measure at all. You need to restrict the user privileges at the data level, using Accounts and Privileges.
Yes, I can restrict the rights via a privilege set, however, I think since the Find and Replace is navigating on the current layout, if a field did not allow Browse access on that layout, the Replace should not work.
Thanks for the help.
Not allowing browse access to a field on a layout is a UI feature. You can overrule it with a script. If you don't want that then don't make such a script.
Use Custom Menus to remove the Find/Replace menu item from the menu set installed for users, either on the layout settings or as the default menu set.
Custome Menus (FM Advanced tool) also allow you to remove or replace the commands for other dangerous items (i.e. Delete All Records, Replace Field Content [across found set], Delete Record [add your scripted tests], View>Layout Mode, etc.).
I never give users the Standard FileMaker Menu Set. There are just too may dangerous commands there for the non-develper to be trusted not to abuse or test.