I recently learned the details of this, and had a thread posted up here asking about it too.
The best I can tell is that you can take your karma just as high on a red as on a blue. A key difference though is that your paperdoll will never display karma-related titles above neutral. On a red the karma can be there, but the char will never display "glorious" anything.
A way to help judge where your red is at karma-wise is to kill liches and lich lords. Liches grant less karma than lich lords do. If you start out with neutral karma, you'll see both of them giving you a "lot" of karma. Then, you'll progress to where the lich is giving you "some" karma, and then eventually the lich will give you no additional karma at all. Then, the lich lords will eventually move from giving you a lot of karma to "some". You've reached a nice karma level when that happens.
One way to observe the effects of your karma on your chivalry spells is by checking how long your Divine Fury lasts. You mouse hover over the icon in your "buffs bar" as soon as you cast Divine Fury and can see the number of seconds that remain on the spell's effect. With my red at 75 chiv, I get my Divine Fury spell to last for 21 seconds according to that buffs bar timer thingie. I was getting 18 seconds somewhere around neutral or low-ish karma, and that had changed to 21 seconds after I'd been beating lich lords around for a good while.
The karma-affected chivalry spells appear to act the same for a red as they do on a blue. I can tell this by doing the above-described test on a pair of high-karma blue and red chars with similar levels of Chiv skill and comparing the results.