You could try to allow it for RAI, but Rending Claws doesn't give you the Rend special ability needed to fulfill it.
Even so, Rending Claws and Improved Rending Fury function almost identically it borderlines being able to stack it.
Is it broken to allow it? Not really, considering it's about as broken as adding a Shocking Weapon Property to your attacks, which is weak in itself. But it's a question of whether the effects would actually stack, since they both work as precision damage from the same source (a feat).
Of course, one could be cheap enough to have a Rend Attack in addition to Rending Claws and the whole Rending Fury feat; dealing 2 Claws (assume Large, 1D6) plus Strength for each. Add in Rend (1D6+(1.5)Strength) plus Rending Claws (1D6) plus Improved Rending Fury (1D6) plus Bleed from Greater Rending Fury (1D6/round until healed). Equating to at best 5D6 + (3.5)Strength + 1D6/Subsequent Round.
A brutal full attack in the lower levels, but is trivialized with high AC and Crane Style. Most of it is not multiplied on a critical hit (only the base Claws are multiplied; Rend is not an attack roll of itself that can be criticaled and the other effects are precision damage).
I actually asked this in a thread a while back. I don't think there's really a consensus. It depends on whether being able to rend with your claws now means you have the "rend" special attack. Frankly it's not something that's answered directly in the rules. Arguments exist on both sides. Expect table variation.
Personally, I'd allow it because it's a substantial feat investment for not a great payoff. It's more of a flavor build than an impact thing, so why not.