ΔE 17.6, loose: different enough that you should pick on purpose. Cultist Purple is noticeably darker, much more saturated than Mauve.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Cultist Purple is noticeably darker, much more saturated than Mauve.
The same difference applies the other way round: Mauve is noticeably lighter, much more muted.
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 Mauve on the colour wheel See Cultist Purple on the colour wheel
All matches: Mauve equivalents · Cultist Purple equivalents