Pandaren mounts are available on their corresponding race. Create a new character and you can get them without the standing.
Cataclysm
3 / 3Complete
Hellscream's ReachNo standing yet
1 / 1
RamkahenNeutral · 2,000 / 3,000
2 / 2
Wrath of the Lich King
5 / 5Complete
The Sons of HodirNo standing yet
2 / 2
The SunreaversRevered · 7,582 / 21,000
2 / 2
The Wyrmrest AccordNeutral · 325 / 3,000
1 / 1
The Burning Crusade
16 / 16Complete
Cenarion ExpeditionNeutral · 1,125 / 3,000
1 / 1
NetherwingNo standing yet
6 / 6
Sha'tari SkyguardNo standing yet
5 / 5
The Mag'harUnfriendly · 2,620 / 3,000
4 / 4
Horde
53 / 53Complete
Bilgewater CartelFriendly · 299 / 6,000
1 / 1
Darkspear TrollsNeutral · 699 / 3,000
8 / 8
OrgrimmarNeutral · 928 / 3,000
18 / 18
Silvermoon CityFriendly · 1,199 / 6,000
9 / 9
Thunder BluffNeutral · 699 / 3,000
8 / 8
UndercityFriendly · 299 / 6,000
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 7 hours ago. Some mounts may be missing or incorrect still. Please report any issues on the contact page.