Filter without having the colors change

I'm having a hard time envisioning what changes you make to the data that could be causing the colors to change. If you just filter, the colors won't change. That is, if you filter on a name (no names are visible in your screenshot but you mention names), those names will still have the same colors they did before you filtered them.

If the rank changes and you re-sort based on rank, then yes, the colors would change. One way to deal with that is to use conditional formatting for the colors. You would need one conditional formatting rule for each color section. For example you would set up a rule having a yellow fill color for A:C (or whatever your columns are):

=AND(2<=ROW(A1),ROW(A1)<=17)

This will always make rows 2:17 yellow no matter how you sort.

It is not clear what you want this to look like when you filter.

It would save time if you could provide your file. An image attachment has limited value. Just attach the Excel file. It's easier than taking a screenshot first and then attaching that. The paper clip icon does not work for attachments. To attach a file, under the text box where you type your reply click the Go Advanced button. On the next screen scroll down and click on Manage Attachments, which will show a pop-up window to Select and Upload a file. Then close the window.

Your actual file is more complicated than what is suggested by your screenshot. You have labels in the left column giving top 10% and quartiles, but they don't seem lined up quite right. Will you always have the same number of rows?

The solution I attached assumes the number of rows is always the same. If not, you will have to adjust the formulas to count the rows and calculate how many is 10% and 20%.