Dragging Validated Value with Protection

[saltnsnails]

I have a Worksheet that employees will select their initials from a
validation list for a given time frame. Those initials are then counted for
each time period per initial at the top of the sheet. I need to have the
count calculations protected.

I want the employess to be able to drag their initials across columns
(rather than click each cell and choose from the list or type)but when I put
the protection on the sheet it does not let me do that even though those
cells are not locked. I only have the count formula cells locked.

Any ideas?
Thanks!