You are speaking about a close range perspective effect. Those parallel lines will straighten out when the observer recedes away from them. The distance does matter.
Yes, the distance does matter. As does the length and angle of the lines/sun rays. The angle you perceive parallel lines to be at with respect to each other depends on all these things. Sun rays are long and can be at a steep angle, even from a distance that can cause a perspective effect.
Sometimes you can get an effect in a wood where crepuscular rays can look as if they're coming from just above the trees.
Obviously in real life you know that's not where the sun is.
How does that work when the camera is miles away like in the image of the crepuscular rays over the island which are clearly miles away?
It works by the rays being long and at a steep angle towards the viewer.
If crepuscular rays are not a perspective effect then what are anti-crepuscular rays? In that phenomenon it appears there must be multiple light sources. Again, in real life you know there isn't and it's just a perspective effect as the parallel rays recede into the distance.
EA occurs over hundreds and thousands of miles.
But if those rays are coming from the sun which is thousands of miles high in your model those rays must be hundreds or thousands of miles long.
You'd surely see some effect.