@gpnphwpd7d2s
Well, yeah, you're right and that takes care of the obvious :D. What can I say, it was late, I was tired, and I just missed it. Duh! So..... New day, I'm awake and thinking again.
Most likely, it might be something else in your mods folder could be interfering with it in live mode. The easy way to check is to rename your current The Sims 4 folder and start the game to let it generate a new one. Then after making and placing the sim. Save and exit. Then put the hair that is causing the problem in the new game's mod folder by itself and restart the game. Put the hair on a sim and go to live mode to see if shows up. If it doesn't, it's the hair. If it does, it has to be something else in your mods folder interfering with it. CC 3D eyelashes, earrings, tattoos, piercings would be the first things I would check as possible causes. A while back, I had a CC tattoo, that after one of the updates, still looked great in CAS but in live mode it turned the sims it was on completely black. It took me a while to figure out it was a tattoo doing that. Once I found and removed it, the sims were back to normal. You might have something similar going on and if that is the case, you're going to have to go through you CC to find the troublemaker.
If that doesn't work to get the hair to display properly, another thing it could be is that it is old and predates the additional color swatches that were added a while ago. To check that, take a look to see if it has the same number of color swatches that game hairs do just to make sure it was made since the update that added the extra colors. You can also take a look what happens when you click the match hair button on the eyebrows to see if the colors match too. If it's a male hair, you can also do that with facial hair. Another way is to switch hairstyles in CAS back and forth with a game hair to see if the hair shows the same color as a game hair for each swatch. A lot of them don't though but work perfectly fine but what you're checking for is that each swatch gets used. It could be that the creator didn't use one and live mode is grabbing that unused swatch for some reason rather than the color you chose. Long shot really but I've seen stranger things happen with CC.
If none of that works, come back and let me know and we'll go from there.
Hope this helps.