A family of Microsoft word processing software products for creating web, email, and print documents.
If you create a character style based on "underlying properties" and you make sure that it doesn't include anything but red color, you can apply that character style to any text range.
To ensure that you don't get any undesired formatting into the character style when you create it, do the following: Select a text range and press Ctrl+SpaceBar to clear any direct font formatting which may be applied to the range. Apply the color red (in this example). Finally, create the character style.
Of course, it remains true that you can't format a text range with a character style and also keep any direct font formatting applied to that same text range, which may or may be relevant to your situation. Character styles will always remove underlying font formatting unless that formatting comes from a paragraph style.