First off, I tried to attach a picture (PNG & JPG) but it keeps saying wrong format, even though I've uploaded a JPG before, so I'll try explaining as best I can without a picture. The size was only 102 KB, so that wasn't the issue either.

I've been trying to change a character's race in my platoon. I have been following a guide but what they are saying is not what I'm seeing when I open the platoon file. From my understanding, when opening items like CHARACTER_APPEARANCE, the right side should be populated with different fields, but all I see is a wall of gray with no options. The game is installed via Galaxy so the FCS and game should be up-to-date.

Any help will be appreciated, thanks!

Well, i never tried to change a characters race via the FCS.
I've now just opened (open any) a random savegame "nameless_x.platoon" file, right-clicked on the header and switched "show type" to ON.
When i doubleclick any of the "character appearance" entries (Name "0"), it will open a new window, with all the settings from the character editor in the left half and a single entry on the right. That's the race entry,in my case showing:

17946-stick_people.mod 0 0 0
(Skeleton Race)

in red letters.
But then i can't change this entry, because the field above (where you can add things), is greyed out.

Why do you want to change the race in the first place?
You can just dismiss a character/race you don't like, hire a new one and if the game allows it, you can edit his appearance right away or later visit a plastic surgeon.