Edited: This answer only covers how to make the code in the linked question actually work. I couldn't enable AA.
You'll need to set the culling to clockwise.
GraphicsDevice.RasterizerState = new RasterizerState
{
CullMode = CullMode.CullClockwiseFace
};
If that messes up your other primitives, you can simply reverse the order of the paths from
path.Add(new VertexPositionColor(new Vector3(curvePoints[x] + normal * curveWidth, 0), Color.Firebrick));
path.Add(new VertexPositionColor(new Vector3(curvePoints[x] + normal * -curveWidth, 0), Color.Firebrick));
to
path.Add(new VertexPositionColor(new Vector3(curvePoints[x] + normal * -curveWidth, 0), Color.Firebrick));
path.Add(new VertexPositionColor(new Vector3(curvePoints[x] + normal * curveWidth, 0), Color.Firebrick));
I'm using VertexPositionColor
because I want a different color.