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)
Vivillon Fancy and Vivillon Pokeball patterns
Magearna and Magearna Original Colour
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.