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 · 500 / 3,000
2 / 2
Wrath of the Lich King
2 / 5
The Sons of HodirNo standing yet
1 / 2
The SunreaversRevered · 4,113 / 21,000
0 / 2
The Wyrmrest AccordNeutral · 650 / 3,000
1 / 1
The Burning Crusade
0 / 16
Cenarion ExpeditionFriendly · 5,036 / 6,000
0 / 1
NetherwingNeutral · 850 / 3,000
0 / 6
Sha'tari SkyguardNo standing yet
0 / 5
The Mag'harNo standing yet
0 / 4
Horde
43 / 53
Bilgewater CartelFriendly · 4,511 / 6,000
0 / 1
Darkspear TrollsFriendly · 4,098 / 6,000
6 / 8
OrgrimmarHonored · 2,564 / 12,000
16 / 18
Silvermoon CityFriendly · 1,000 / 6,000
8 / 9
Thunder BluffHonored · 511 / 12,000
6 / 8
UndercityFriendly · 4,436 / 6,000
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, 1 day ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.