You do understand that "not supported" does not mean prohibited or banned don't you? That's pretty weak language. Let me give you a couple examples of more concrete language from Section 115:
The Captain is, and shall always be, the final authority as to admission to the flight deck.
Accordingly, ALPA supports the Captain's authority to exclude any person other than required crew from the flight deck if, in his opinion, that person's presence will compromise safety.
The presence of a non-Union pilot who is actively undercutting my contract is a distraction that compromises safety.
Host Captains should recognize that a union membership card is another means of identity verification, although not all pilots of represented airlines are union members.
So Section 115 says I CAN use a Union Card as additional identification.
Under the Captain's authority, entry to the flight deck will not be permitted for individuals with whom the Captain or his flight deck crew is not entirely comfortable.
A non-Union pilot who is actively undercutting my contract isn't the kind of person I'm comfortable with.
So, it looks like your "buddies" who "wrote" Section 115 gave me plenty of leeway to accept or deny anyone I want for jumpseat privileges, while reserving the weakest language ["not supported"] for those of you who seem to think the jumpseat is a right conferred upon you by your pilot's license.