As of Generation 9, the following Pokemon cannot be shiny under any circumstances:
Any Ash-hat Pikachu (technically can be, but coloration does not change. Credit to Y for that one)
Victini
Keldeo
Meloetta
Ash-Greninja
Vivillon Pokeball pattern
Hoopa
Volcanion
Cosmog
Cosmoem
Magearna and Magearna Original Colour
Marshadow
Kubfu
Urshifu
Zarude
Glastrier
Spectrier
Calyrex
Enamorus
Ting-Lu
Chien-Pao
Wo-Chien
Chi-Yu
Koraidon
Miraidon
Walking Wake
Iron Leaves
Okidogi
Munkidori
Fezandipti
Ogerpon
Gouging Fire
Raging Bolt
Iron Boulder
Iron Crown
Terapagos
Pecharunt
The Galar starters are also only obtainable as shinies by breeding --- you cannot soft reset at the start of the game for them.
There are some game-exclusive shiny locks, which can be found in my source.