Note:
Just because a pokemon is in the Never Cleansing category
they will still cleanse their burn, paralysis ect. when the shield goes up
but they will never remove debuffs like stat drops.

5 Star Base Game Pokemon (29/99) that made the list (Complete)

Never Nullifies - Abomasnow
Never Nullifies - Altaria
Never Nullifies - Annihilape
Never Nullifies - Arcanine
Never Nullifies - Brambleghast
Never Nullifies - Braviary
Never Nullifies - Bronzong
Never Nullifies - Cloyster
Never Nullifies - Dragonite
Never Nullifies - Dragalge
Never Nullifies - Eelektross
Never Nullifies - Florges
Never Nullifies - Froslass
Never Nullifies - Gallade
Never Nullifies - Glalie
Never Nullifies - Glimmora
Never Nullifies - Gyarados
Never Nullifies - Hatterene
Never Nullifies - Houndoom
Never Nullifies - Hydreigon
Never Nullifies - Luxray
Never Nullifies - Oranguru
Never Nullifies - Polteageist
Never Nullifies - Revavroom
Never Nullifies - Slaking
Never Nullifies - Tinkaton
Never Nullifies - Tyranitar
Never Nullifies - Volcarona
Never Nullifies - Weavile

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5 Star Teal Mask Pokemon (15/25) that made the list (Complete)

Never Cleanses - Ambipom
Never Cleanses - Basculegion (Female)
Never Cleanses - Chandelure
Never Cleanses - Gliscor
Never Cleanses - Golem
Never Cleanses - Mandibuzz
Never Cleanses - Mienshao

Never Nullifies - Basculegion (Male)
Never Nullifies - Conkeldurr
Never Nullifies - Ludicolo
Never Nullifies - Mamoswine
Never Nullifies - Probopass
Never Nullifies - Sinistcha
Never Nullifies - Trevenant
Never Nullifies - Vikavolt

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5 Star Indigo Disk Pokemon (18/21) that made the list (Complete)

Does Neither - Alcreamie (Cleansing/Nullifying)
Does Neither - Flygon (Cleansing/Nullifying)

Never Cleanses - Golurk
Never Cleanses - Minior
Never Cleanses - Porygon-Z

Never Nullifies - Duraludon
Never Nullifies - Electivire
Never Nullifies - Excadrill
Never Nullifies - Exeggutor
Never Nullifies - Hitmonchan
Never Nullifies - Hitmonlee
Never Nullifies - Hitmontop
Never Nullifies - Lapras
Never Nullifies - Metagross
Never Nullifies - Porygon2
Never Nullifies - Reuniclus
Never Nullifies - Rhyperior
Never Nullifies - Skarmory

6 Star Base Game Pokemon (3/70) that made the list (Complete)

Never Nullifies - Dragalge
Never Nullifies - Gallade
Never Nullifies - Revavroom

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6 Star Teal Mask Pokemon (18/28) that made the list (Complete)

Never Cleanses - Ambipom
Never Cleanses - Gliscor
Never Cleanses - Mandibuzz
Never Cleanses - Mienshao
Never Cleanses - Milotic
Never Cleanses - Morpeko
Never Cleanses - Ninetales
Never Cleanses - Shiftry
Never Cleanses - Trevenant

Never Nullifies - Clefable
Never Nullifies - Dusknoir
Never Nullifies - Golem
Never Nullifies - Leavanny
Never Nullifies - Ludicolo
Never Nullifies - Mamoswine
Never Nullifies - Sinistcha
Never Nullifies - Snorlax
Never Nullifies - Yanmega

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6 Star Indigo Disk Pokemon (17/27) that made the list (Complete)

Does Neither - Metagross (Cleansing/Nullifying)
Does Neither - Rhyperior (Cleansing/Nullifying)

Never Cleanses - A-Exeggutor
Never Cleanses - Alcreamie
Never Cleanses - Kleavor
Never Cleanses - Magmortar
Never Cleanses - Reuniclus

Never Nullifies - A-Dugtrio
Never Nullifies - A-Golem
Never Nullifies - A-Ninetales
Never Nullifies - Duraludon
Never Nullifies - Excadrill
Never Nullifies - Flygon
Never Nullifies - Kingdra
Never Nullifies - Malamar
Never Nullifies - Overqwil
Never Nullifies - Whimsicott

Hope it all looks nice and clean, I'm pretty confident that I didn't miss any
which is why i gave the list (Complete) staple treatment
but there is always the off chance I missed one or two
so if you do find any I did miss don't hesitate to let me know so I can add it to the list.

Hopefully you might benefit from it as I'm sure I most definitely will.