ΔE 18.5, loose: different enough that you should pick on purpose. Kakophoni Purple is a little darker, more saturated, warmer than Cultist Purple.
✓ Two Thin Coats comparison chart lists these two as equivalents.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Kakophoni Purple is a little darker, more saturated, warmer than Cultist Purple.
The same difference applies the other way round: Cultist Purple is a little lighter, more muted, 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 Kakophoni Purple on the colour wheel
All matches: Cultist Purple equivalents · Kakophoni Purple equivalents