ΔE 19.9, loose: different enough that you should pick on purpose. Violet Skies is noticeably lighter, warmer than Cultist Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 20). Violet Skies is noticeably lighter, warmer than Cultist Purple.
The same difference applies the other way round: Cultist Purple is noticeably darker, cooler.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Cultist Purple on the colour wheel See Violet Skies on the colour wheel
All matches: Cultist Purple equivalents · Violet Skies equivalents