I agree with Lockwelle, however you seem to be specifically concerned with fields being moved.
To prevent that isssue specifically, right click on a field (or multiple field selection)
Select Format
Ont he Common Tab there is an option to "Lock Position and Size"
Mark that as TRUE
I do not know how to do that for all fields in the report at once but you can try section by section with multiple field activation.
Note: users can still delete the field but they cannot move it.