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 ReachNo standing yet
0 / 1
RamkahenNeutral · 900 / 3,000
2 / 2
Wrath of the Lich King
5 / 5Complete
The Sons of HodirHated · 1,300 / 36,000
2 / 2
The SunreaversHonored · 6,631 / 12,000
2 / 2
The Wyrmrest AccordFriendly · 1,251 / 6,000
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionHonored · 700 / 12,000
1 / 1
NetherwingNo standing yet
6 / 6
Sha'tari SkyguardNo standing yet
5 / 5
The Mag'harNo standing yet
4 / 4
Horde
53 / 53Complete
Bilgewater CartelHonored · 674 / 12,000
1 / 1
Darkspear TrollsRevered · 15,028 / 21,000
8 / 8
OrgrimmarHonored · 5,719 / 12,000
18 / 18
Silvermoon CityHonored · 879 / 12,000
9 / 9
Thunder BluffHonored · 2,523 / 12,000
8 / 8
UndercityHonored · 1,174 / 12,000
9 / 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 1 hour ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.