Just ignore the cohealer and do whatever. If you suck, then the other healer will complain. If you both suck, then the party will wipe and everyone will complain. As long as nobody is complaining, you're fine. If both healers start the raid fights in cleric stance, then you know it's going to be harder because neither healer is prioritizing healing.

As a healer you should be putting healing before DPS, because healing works a lot better in tandem (eg Cure I + Psysick is less MP intensive than you using Cure II on everyone.) That said, everyone is overgeared, so unless you're playing Coil, with the current gear people have, most content should be solo-healer capable.

And remember, if players are playing bad on purpose, you don't need to pull their butt out of the fire every single time. If someone keeps dying, then it's actually easier for the Scholar to keep resurrecting them if they are using Aetherflow frequently (60 second cooldown, instant effect,) than it is the WHM to keep raising dead players, since the WHM would have up to 2 minutes of cooldown plus have to wait for the MP to recover before casting raise from 0 MP.

The only real difference in 24-person raids over light parties is that only one party's tank is "main tank", so if you're in that party, one healer should be prioritizing the tank because delaying their healing might wipe the raid. If you're in any of the other parties, then know the mechanics and save the healbombs for incoming damage.