Is it possible to prevent conditional formatting ranges from breaking when you copy/cut data to and from the range?

I currently have a conditional formatting rule set up for range $1:$1. However, this will break (and subsequently cause a lot of lag) if I copy a cell from a different row and paste it into row 1, or cut a cell from row 1 and paste it to a different row. I'm aware this is because I'm pasting the formatting and that's overriding the rule. Is there a way to make Excel not do that?

I'm aware of pasting values not breaking the formatting; however sometimes there are things like borders which I want to copy over without having to mirror the formatting manually.