So I'm trying to use the drop-down menus to restrict human input, but there is a formula than can fill in those cells with information that I don't want humans to be able to enter in. The formula does that just fine, but the problem is that when it triggers it also gives an error message because that input option is not on the drown list. Is it possible to either stop the error from occurring or some other work around to not show that red triangle in the corner of the cell?
Just remove the data validation from the cells that contain a formula.
Regarding your specific question, there is no way to remove the data validation indicator that the cell value is invalid when the value actually is invalid.