FairyTWBtW: Being restricted to light armor is rough, but the mobility flight offers when playing a support character is hard to ignore.
FirbolgVGtM: Strength and Wisdom bonuses play well to your strengths. The passive abilities and spellcasting are quite useful.
GenasiEEPC: The Constitution bonus is useful, but all the other abilities are either situational or useless.
Air: Nothing useful for the Cleric.
Earth: Nothing useful for the Cleric.
Fire: Nothing useful for the Cleric.
Water: The Wisdom bonus makes this the only useful Genasi subrace worth considering.
GithMToF: both Gith subraces make excellent Cleric builds.
Githyanki: Strength bonus, weapon proficiencies, and spellcasting make a good melee Cleric build.
Githzerai: Wisdom increase, Mental Discipline, and spellcasting make a great support Cleric.
Gnome: Gnomes don’t gain any useful abilities for Clerics.
Deep (Svirfneblin)EEPC/SCAG: Nothing useful for the Cleric.
Forest: Nothing useful for the Cleric.
Rock: Nothing useful for the Cleric.
GoblinVGtM: Nothing useful for the Cleric.
GoliathVGtM/EEPC: Goliaths make resilient and beastly melee clerics, but their prominence diminishes your role as a support character.
Half-Elf: Half Elves make a decent choice for any class. The Charisma bonus is wasted on a Cleric, but the flexibility provided means you can choose to spec for whatever type of character you’re looking to play.
Standard: the choice of skills allows you to make up for whatever you’re lacking in class or background skills.
AquaticSACG: Useful in an aquatic campaign.
DrowSCAG: Access to faerie fire is useful.
Moon/SunSCAG: Access to wizard cantrips is useful.
WoodSCAG: Access to a better weapon option is good for a melee build, but a different race would provide a better advantage.
Half-Orc: Nothing useful for the Cleric.
Halfling: Not a strong choice for Cleric.
Lightfoot: Nothing useful for the Cleric.
GhostwiseSCAG: Trickery domain clerics see a little bit of synergy here.
Stout: Nothing useful for the Cleric.
HarengonTWBtW: Quick initiative is important for a support character looking to set up buffs and position.
HexbloodVRGtR: This race grants you a few spells which aren’t very commonly used by clerics, but are useful none the less
HobgoblinVGtM: Nothing useful for the Cleric.