There is no way to describe the issue, that's why I'm just going to show the rendered image:
Those are 4 planes with no modifiers, the same dimensions, the same particles, and the same material. The only difference is the topology. All planes are hidden - only the hair is visible.
Number 1 is a simple plane
Number 2 is a plane with loop cuts (Ctrl + R)
Number 3 is extruded (I started with a small plane and made it bigger with extrusions)
Number 4 is the same as Num.3 but the cuts are made with "Knife projection"
Numbers 1 and 2 are good, the issues are in 3 and 4
All faces have the same normals. I tied recalculating the normals, I also tried flipping them - nothing worked.
Just in case anyone asks - I'm making a big project and the model with the hair is very complex (I used extrusions, knife projections, and more) that's why I need to fix it without retopologizing the whole mesh. Because the project file is big I made this .blend file with the planes where I recreated the same issue.
Here is the .blend file: