I will just drop a small lecture.
The Knights of the Silver Hand, was the Paladin Order made by Uther Lightbringer during the FIRST WAR, but yea skipping history lessons...
The organization accepts bound races to the light and able to wield the virtues of being Paladins :
Races that CAN be Paladins :
Humans : They have made the order, figure that.
Dwarves : Trained by Humans in the past.
High Elves : Trained by Humans
Blood Elves : Sunwell.
Tauren : They have their own view of the Light through Anshe
Draenei : Blessed by their Naaru
Races that is POSSIBLE to become :
Worgen : Gilnean people did not need Paladins during the wars, but there is nowhere restricting them from becoming Paladins, knowing that from Cataclysm til Legion, 4-5 Years passed and it is possible to become a member.
Gnomes : A rare case, they could have picked up training from the Dwarves, but its much more harder to wield their armor and power.
Night Elf : VERY RARE case, it would involve the elf to not have ties with the moonwell, in my opinion.
Races that CANNOT become :
Undead : The sheer amount of holy energy would kill the Undead dude instantly or through time.
Trolls : Their deity, beliefs and culture do not allow Trolls to even remotely become Paladins.
Goblins : Why would a Bilgewater cartel member, focused on gold and blowing s*it up become a weapon of justice? Reminds me of that Gilnean Goblin I've seen on RPH. No.
Orcs : The Orcish culture trains them to become fierce warriors and people, they don't waste their time training the important virtues and morals of the light. Their blood-lust does not allow them.
Pandaren : The culture of Pandaren have no infrastructure compared to Humans to even have knowledge such thing existed, they base their life on a different views than ours. No.