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 · 2,200 / 3,000
2 / 2
Wrath of the Lich King
3 / 5
The Sons of HodirNo standing yet
2 / 2
The SunreaversHonored · 709 / 12,000
0 / 2
The Wyrmrest AccordNeutral · 1,072 / 3,000
1 / 1
The Burning Crusade
9 / 16
Cenarion ExpeditionHonored · 402 / 12,000
0 / 1
NetherwingNo standing yet
0 / 6
Sha'tari SkyguardNo standing yet
5 / 5
The Mag'harFriendly · 3,179 / 6,000
4 / 4
Horde
43 / 53
Bilgewater CartelHonored · 1,429 / 12,000
0 / 1
Darkspear TrollsFriendly · 5,999 / 6,000
6 / 8
OrgrimmarHonored · 7,202 / 12,000
16 / 18
Silvermoon CityHonored · 2,815 / 12,000
7 / 9
Thunder BluffFriendly · 5,999 / 6,000
7 / 8
UndercityRevered · 16,804 / 21,000
7 / 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 2 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.