As a slight improvement on @ajlittoz's suggestion to use styles, you might use Find & Replace (ctrl-h) to select only the colored text, apply a paragraph or character style, and then clear direct formatting. You could also do the same for any other formatting attribute that the dialog can handle. This could save a lot of time depending on the complexity of the text, and also assures that you don't miss anything.
Case 1) If there is only one color, open "Other Options", click the Attributes button and select font color, make sure the "find" text is empty, and click Find All. Then apply the style.
Case 2) If there are multiple colors that need to be preserved, it looks like you should be able to do the same thing one color at a time. Click the Format button and go Font Effects > Font Color > Custom Color and enter the RGB value, then precede as before. Obviously, you'll have to examine the target text first to find out the color.
Note: I find the Find & Replace dialog is quite fiddly and hard to use. I think Case (1) is more likely to be worth the trouble than Case (2), but if the text is sufficiently complex then this strategy may well be worth it even in the latter case.
