Every passive ability has a hidden rank: putting aside red-locked abilities, abilities with higher ranks take precedence over abilities with lower ranks. sakurayule's Monster FAQ has a list of all the ranks in the game, but the list you see in game corresponds to this precedence:
- Red-locked Stagger Maintenance II
- Yellow-locked Feral Speed II (rank 16)
- Role Resonance (rank 7)
- Item Collector (rank 6)
- Resist Deshell +66% (rank 6)
- Resist Ice +45% (rank 5)
- Resist Fire +45% (rank 5)
- Critical: Bravery (rank 5)
- Resist Deprotect +44% (rank 4)
- Pack Mentality (rank 4)
Strength +35% has a rank of 7, which means it would take precedence over everything except Role Resonance and the yellow-locked Feral Speed II. If you infused your Red Chocobo with it right now, you will lose Pack Mentality.
The only way to prevent this would be to yellow-lock Pack Mentality so it gains a higher precedence. Unfortunately, there are only two monsters in the game that have an infusable Pack Mentality—Chichu and Nanochu—and both are unique crystals.1 If you've already used both crystals, or you were hoping to use the crystals on different monsters, you are indeed out of luck.
Note 1: Unless you purchase the Perpetual Battlefield DLC, which allows you to fight Valfodr. The drops for defeating Valfodr at level 70 include monster crystals for both Nanochu and Chichu.