Pandaren mounts are available on their corresponding race. Create a new character and you can get them without the standing.
Cataclysm
2 / 3
Hellscream's ReachFriendly · 5,437 / 6,000
0 / 1
RamkahenNo standing yet
2 / 2
Wrath of the Lich King
0 / 52 to get now
The Sons of HodirNo standing yet
0 / 2
The SunreaversNo standing yet
0 / 2
The Wyrmrest AccordFriendly · 1,114 / 6,000
0 / 1
The Burning Crusade
5 / 16
Cenarion ExpeditionFriendly · 5,332 / 6,000
0 / 1
NetherwingNo standing yet
0 / 6
Sha'tari SkyguardNo standing yet
5 / 5
The Mag'harNeutral · 587 / 3,000
0 / 4
Horde
37 / 535 to get now
Bilgewater CartelFriendly · 3,136 / 6,000
0 / 1
Darkspear TrollsFriendly · 1,550 / 6,000
6 / 8
OrgrimmarRevered · 6,947 / 21,000
16 / 18
Silvermoon CityFriendly · 1,401 / 6,000
7 / 9
Thunder BluffFriendly · 4,901 / 6,000
3 / 8
UndercityFriendly · 4,001 / 6,000
5 / 9
Darkspear Trolls and Orgrimmar and Silvermoon City and Thunder Bluff and Undercity mounts are available on their corresponding race. Create a new character and you can get them without the standing.
Standings come from the last update, about 7 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.