As of Generation 8, the following Pokemon cannot be shiny:
Any Ash-hat Pikachu (technically can be, but coloration does not change. Credit to Y for that one)
Victini
Keldeo
Meloetta
Vivillon Fancy and Vivillon Pokeball patterns
Hoopa
Volcanion
Cosmog
Cosmoem
Magearna and Magearna Original Colour
Marshadow
Zacian
Zamazenta
Eternatus
Kubfu
Urshifu
Zarude
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 more, which can be found in my source.