At some point, a large number of entirely unobtainable shiny pokemon were changed to be able to be marked as obtainable in the Pokemon Home Living Dex page. Some pokemon remained marked as unobtainable, such as Greninja (Battle Bond) and Zarude (Dada), but the following pokemon are still unobtainable shiny but have been marked as obtainable:

Victini

Vivillon (Pokeball Pattern)

Hoopa

Hoopa (Unbound)

Volcanion

Cosmog

Cosmoem

Magearna

Magearna (Original)

Marshadow

Kubfu

Urshifu (Single Strike)

Urshifu (Rapid Strike)

Zarude

Glastrier

Spectrier

Calyrex

Ursaluna (Blood Moon)

Walking Wake

Iron Leaves

Okidogi

Munkidori

Fezandipiti

Ogerpon

Gouging Fire

Raging Bolt

Iron Boulder

Iron Crown

Terapagos

Technically Koraidon, Miraidon, and Chi-Yu are also currently unobtainable shiny, but have events releasing soon to obtain them, so I didn't include them on this list.