I'd simply allow the more beneficial effect to take precedence. So because Protection from Energy is better than Warding Bond against the breath weapon, PfE applies. If the dragon claws the fighter, Warding Bond applies.
Exactly, the rules are not magic the gathering cards this edition, there will be issues like this for the DM to pass judgement on.
I wouldn't allow the cleric to benefit from PfE though. It says "you take the same amount of damage" but nothing about damage type, so I'd rule that the shared damage from WB is untyped and therefore unable to be reduced by PfE.
Agree, any share the damage type effects should treat the shared damage as untyped to prevent resistance stacking.