original image -> convert to linear color space -> multiply alpha -> blur -> composite -> possibly convert back to sRGB if needed
The wrong way I meant was
original image -> multiply alpha -> gamma-correct-blur -> composite
where gamma-correct-blur = convert to linear color space -> blur filter -> convert to sRGB
original image -> convert to linear color space -> multiply alpha -> blur -> composite -> possibly convert back to sRGB if needed
The wrong way I meant was
original image -> multiply alpha -> gamma-correct-blur -> composite
where gamma-correct-blur = convert to linear color space -> blur filter -> convert to sRGB