Well that is later on, so far Axel was proven to be loyal, he killed traitors to the Order. My guess is he eventually learns that the Order is being manipulated and betrays it. Hence the "You're being used by the Order." The members itself are probably good just, again, being used by a higher up power, probably EM. From the looks of thing this is showing that DiZ and Ansem are far from the same person and chances are, DiZ and Ansem (who might be EM) are using the Org to do things for them. Axel probably learns this and defects, thus maybe why Axel calls himself a "friend" of Sora. Sora is against Ansem, so they both share a common goal maybe?
What I ment by the Order not being bad was, aside from possible manipulation, the known members mostly seem to not be evil, while they might not be doing things in the best way, they aren't seeking Kingdom Hearts for the same reasons as Ansem. They just want to become human so far, so for now they aren't really evil, just misunderstood.
As for Axels loyalalty, again I believe he is VERY loyal, just learns what is really happening. Again he reminds me of Inferno from Beast Wars. I don't think Axel was in the Org planning on betraying them, or manipulating them and I REALLY doubt he is working for DiZ. During the events of CoM Axel role in the Org was like that of the Teachers Pet, he seemed to want nothing more then to support the Org and its Leader. The way he killed the betrayer and his words in CoM. Granted he might be a little hot headed, but again I just think he realizes he's a pawn in the end and decides to bite the hand that's been feeding him.