Ok here is my very personal way to solve this
after drawing your hairs you need to check "fill caps" in spline shape
then convert your hairs to mesh with good resolution for simulation
Hit tab button and hit "a" button to select all your hair and hit "m" and by distance , and hit "Shift + n"
create a vertex group and ...
Honestly, I don't know why this flipping happens. But you can use the Particle Instance modifier instead of the Rendered as Object method. The advantage is that the grass does not flip and it can bend in the direction of the wind (and not to the left or right).
To use the Particle Instance modifier method to the following:
in the Particle Settings of the ...
You could try this:
Create a UV sphere (here 16/8 vertices), cut it off, extrude the faces to give it thickness:
Pull down the edges to create hair peaks:
Scale 1 out of 2 edges:
maybe triangulate the topology with CtrlT or try the Decimate modifier: