Here are the races I’m thinking would be allowed to become specialty priests. When a majority of the priesthood is one race over the others, I’ve noted it with an asterisk.
Nebelun – Gnomes: Rock*, forest, svirfneblin, tinkers*
Gruumsh – Orcish blood: Orcs*, half-orcs, orogs*, scro, ogrillon, cyclops & cyclopskin
Bahgtru – Orcish blood: Orcs*, half-orcs, orogs*, scro, ogrillon, ogres
Ilneval – Orcish blood: Orcs*, half-orcs, orogs*, scro, ogrillon
Luthic – Orcish blood: Orcs*, half-orcs*, orogs, scro
Shargaas – Orcish blood: Orcs*, half-orcs*, orogs, scro
Yurtrus – Orcish blood: Orcs*, half-orcs*, orogs, scro
Note: Neo-orogs (Thayan hybrids) and ondonti (peace-loving orcs who worship Eldath) would not be allowed to become specialty priests of any of the orcish gods.
Maglubiyet – Goblins*, hobgoblins, norkers, koalinth
Bargrivyek – Goblins*, hobgoblins, norkers, koalinth
Khugorbaeyag – Goblins*, hobgoblins, norkers, koalinth
Nomog-Geaya – Goblins, hobgoblins*, norkers, koalinth
Hruggek – Bugbears
Grankhul – Bugbears
Skiggaret – Bugbears
Kurtulmak – Kobolds*, urd
Gaknulak – Kobolds*, urd
Kuraulyek – Kobolds, urd*
Meriadar – Mongrelmen*, goblinoids, almost any other race
Stalker – Bugbears*, any goblinoids
Zinzerena – Drow
Diirinka – Derro
Diinkarazan – None
The Elder Elemental God – Humans*, drow*, almost any other race
Juiblex – Aboleth*, humans*, almost any other race
The Dark God – Humans*, almost any other race
Ilsensine – Illithids
Maanzecorian – Illithids
Psilofyr – Myconids*, vegepygmies
Great Mother – Any beholder race
Gzemnid – Renegade beholders
Annam – Cloud*, storm*, stone giants*
Stronmaus – Cloud*, storm*, fog, reef giants
Hiatea – Firbolgs*, voadkyn*, almost any other giant
Grolantor – Hill giants*, ettins, ogres, half-ogres, cyclops, cyclopskin, mountain giants
Iallanis – Any true giant
Karontor – Fomorians*, verbeeg*, almost any other giant
Memnor – Cloud*, fog giants
Skoreaus Stonebones – Stone giants
Diancastra – almost any giant
Baphomet – Minotaurs*, evil giants
Kostchtchie – Frost giants
Vaprak – Ogres*, ogre magi, half-ogres, ogrillon
Yeenoghu – Gnolls*, flinds, ghasts, ghoul lords, vorrs
Gorellik – Gnolls*, flinds
Demogorgon – Ixitxachitl, Ixzan
Jazirian – None (couatl)
Koriel – Ki-rin*, lammasu, shedu, tu’en-rin
Panzuriel – Almost any evil aquatic race (kraken, koalinths, sahuagin, merrow, scrags, vodyanoi, sirines)
Eadro – Mermen*, locathah*, crabmen, shalarin, sirines
Persana – Tritons*, shalarin, sirines
Quorlinn – Kenku*, avariel, aarokocra
Sekolah – Sahuagin*, weresharks
Surminare – Selkies, star selkies
Remnis – Giant Eagles*, aarakocra, avariel
Syranita – Aarakocra*, avariel
Trishina – Sea Elves*, dolphins*, malenti, whales, orca, shalarin, sirines
Water Lion – Any good aquatic races other than malenti
Stillsong – None
Blibdoolpoolp – Kuo-toa
Laogzed – Troglodytes*, blindheims, firenewts, tren
Merrshaulk – Yuan-ti
Ramenos – Bullywugs*, blindheims, firenewts, grippli, grung
Semuanya – Lizard men*, firenewts, laerti, tren
Sess’Innek – Lizard men*, lizard kings, laerti, tren
Parrafaire – Nagas (revered only)
Shekinester – Nagas
Io – None
Aasterinian – Brass, copper, mercury dragons
Bahamut – Gold, silver, bronze, steel dragons
Chronepsis – None
Faluzure – Shadow dragons, dracoliches
Tiamat – Yellow, brown, blue, green, red dragons
Cegilune – Hags
Kanchelsis – Vampires
Mellifleur – Lich-priests, priests wishing to become liches
Squerrik – Wererats
Balador – Werebears
Ferrix – Weretigers
Daragor – Werewolves, seawolves, loup du noir, loup-garou
Eshebala – Werefoxes
Titania – Sprites, brownies, buckawns, hybsils, kercpa, other faeries
Oberon – Sprites, pixies, buckawns, kercpa, faerie-warriors
Caoimhin – None (Killmoulis)
Damh – Satyrs, korreds, atomies
Eachthighern – Unicorns, pegasi, asperii, pegataurs, hippocampi
Emmantiensien – Treants
Fionnghuala – Swanmays
Nathair Sgiathach – Faerie dragons, pseudodragons
Skerrit – Centaurs, pegataurs, chevalls, hybsils
Squelaichie – Leprechauns
Verenestra – Nymphs, dryads, hamadryads, sylphs
The Queen of Air and Darkness – Quicklings, elves, unseelie sprites, other evil faeries
I’m open to additional suggestions, too, of course.