A bar curved in its linear axis will change length when compressed or tensioned, a straight tube won't. Unless it's significantly stiffer than its linked tubes, this bending will allow the others to move.
NHRA doesn't have any structural engineers making these decisions...
True, although the degree of the bend matters. A 10 degree kink in a door bar is not as significant of an issue as a 45 or 60 degree bend I see in some of these photos. On any major tube, I will support any bend over 30 or so with a diagonal of some sort...
Frankly I don't see how some of the bars in the photos got a tag put on them. I don't think that would fly in NHRA D1. And the bends certainly reduce the effectiveness of stiffening the car.
I have done some bars like that for restomods and drivers with the stipulation that it wasn't legal for competition. And the guys who just wanted to sneak into an occasional TnT were OK with that.
There's a difference between "dipping" the bar down to get over it easier and tweaking it out to keep it tight to the door for max driver space. On new cars with the bigger plastic door panels, it's not unusual to shape the side bar to fit the door snug - horizontally out, not dipping it down. Older cars with a flat door panel, I may tweak it up over the door handle, window crank, etc. and/or adjust the bar up or down. They can still be a challenge for an old fat guy to get in and out with the steering wheel and seat in the stock location. But there's only so much wiggle room in the rules and in keeping the thing safe.
Swing out bars are okay when properly done. Attachment angles adjusted so they open flat rather than flop down. They still cost some rigidity, and make window nets a pain. I wouldn't bend a sidebar down excessively unless it was just for looks.
One trick on the swing out is to make it a solid bar to fit the door nice, weld it in, then slice it where you want to make the swing out. Looks much nicer and is easier than working with three separate pieces.