Yes, there is a way to keep the fill colors constant when cut or copying text in Excel. You can use the "Paste Special" feature to achieve this.

Here are the steps to follow:

1. Select the cell(s) that you want to cut or copy.
2. Press "Ctrl + X" to cut or "Ctrl + C" to copy.
3. Select the cell where you want to paste the text.
4. Right-click on the cell and select "Paste Special" from the context menu.
5. In the "Paste Special" dialog box, select "Values" and "Skip Blanks" options.
6. Click on "OK" to paste the text without changing the fill color.

By selecting the "Values" option, you are pasting only the text and not the formatting. And by selecting the "Skip Blanks" option, you are preventing Excel from overwriting the fill color of the destination cell.

You can also use the keyboard shortcut "Alt + E + S + V" to open the "Paste Special" dialog box.