The issue happens when you have conditional formatting applied to some cells,
whose behavior is based on the content of some others cells, which the
conditional formatting formula references using a fixed reference (like "$C$1).

If for any reason you move the cells to another place in the worksheet, the
conditional formatting formula does not get updated. It will still reference the
old cell location. Different ways to "move" the cell include: cut&paste of the
cell, inserting a new column, etc.
Please note that, for normal formulas like: =$C$1+$C$2, the references are
updated in case the cell is moved.
It's only happening to the conditional formatting formulas.

A workaround exists. It's still possible to manually change the references.
But this behavior is confusing: When inserting, for example, a new column... the
user is not expecting such changes in the formating. It could happen he/she
doesn't notice the missbehavior till much later. And then, it will not recognize
why suddenly the formating of their cells happened.

Thanks for your hard work!!