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
The Galar starters are also only obtainable as shinies by breeding -- you cannot sort reset at the start of the game for them.
There are some game-exclusive shiny locks, which can be found in my source.