Longtooth (Su): While shifting, a longtooth shifter gains a +2 bonus to Strength and grows fangs that can be used as a natural weapon, dealing 1d6 points of damage (plus an extra 1 point for every four character levels he has) with a successful bite attack. He cannot attack more than once per round with his bite, even if his base attack bonus is high enough to give him multiple attacks. He can use his bite as a secondary attack (taking a —5 penalty on his attack roll) while wielding a weapon.
Razorclaw (Su): While shifting, a razorclaw shifter gains a +2 bonus to Strength and grows claws that can be used as natural weapons. These claws deal 1d4 points of damage (plus an extra 1 point for every four character levels he has) with each successful attack. He can attack with one claw as a standard action or with two claws as a full attack action (as a primary natural weapon). He cannot attack more than once per round with a single claw, even if his base attack bonus is high enough to give him multiple attacks. He can attack with a claw as a light off-hand weapon while wielding a weapon in his primary hand, but all his attacks in that round take a —2 penalty.
Perhaps I am reading it entirely differently, but the text regarding the bite is
inferring that he can still use his bite attack
in addition to his weapon attacks. Which is no different than the established secondary natural attack quality. The character with the bite attack does not suddenly lose his ability to make a bite attack if he's not conventionally armed with a weapon; in a way, the sentence about not attacking more than once per round with a bite sort of supports that as that is the typical convention when dealing with a natural bite attack.
Building off that, in regard to the claws, it is no different than the standard rules for a claw and a weapon.
In effect you are "two-weapon fighting" in a way while armed with a single weapon and having two natural claw attacks (one is removed because a hand is occupied). Without a weapon, thus just the claws, it is no different than any other natural claw attack - one single attack as a standard action, or two claws as a full attack action.
I don't want to give the impression that a Shifter suddenly has a bunch of unusual exceptions to fairly (in terms of 3.5e's inherent insanity) standardized functions on natural attacks - at least where claw and bite is concerned.
Edit: I
suppose in theory you could force the bite attack to default to a secondary attack in the context of having both claw attacks and a bite - the claws do count as "weapons", albeit natural ones - but there's creatures such as the Smilodon (Frostburn, pg 118) which has a primary bite attack and a secondary set of claw attacks. Sure, degrees of separation and all, but animal types with claw and bite attacks are probably the best frontrunners for examples of execution.