How to use Sheet and Range protection and Conditional formatting simultaneously in Google Sheet?

Here I gave conditional formatting in the column E , with two colors for the users A and B respectively. Now I want to enable access to A and B for their respective cells in columns F and G. I can do it manually. But I want to do the same for future rows of data, which automatically copies the cell protection rules to columns F and G in respect to the user in the column E. How to do it ?

Sample Google Sheet