Abate Light is appearing as a red name for all characters besides my main. What does that mean?
When you abililink with a bot or friend you gain their support abilities as long as you have the job asterisk that they have leveled up. These abililink abilities will be red in your abilities menu.
Quote by KaruShale on GameFAQs:
"... Your friend has trained the jobs: Monk to Lv 2 and Freelancer to Lv 3. And you Abilink it to your White Mage. Now they can equip "Martial Arts" for it's Lv 2 command abilities, and the Freelancer's Lv 3 "Diving Rod" support ability."
Note: KaruShale mentions in the same post that the color is yellow when they are abililink abilities, but from my experience with the EU version, it is red. Maybe it's different depending on the region?
I'll provide a more concrete source when I can.
Source: GameFAQs Forum Topic