The parachute is descending through the air, so, of course the protector will flap around. And, if the parachute generates lift, it may be gliding which also causes air flow around it.
If you look at the video, it's pretty clear that the protector is flapping in a wind, not being blown by the descending through the air. That chute was intentionally built to be oversized, so the descent rate is only about 12 fps at most. The protector is not reacting to a 12 fps descent -- it's flapping in air that is moving horizontally, not vertically.
And I don't think the chute is gliding. I was there watching this flight, and the chute hung in the air steady as a rock. And the rocket came down very close to the launch pads, so I don't think it glided. But if it did glide, then doesn't that mean that not all chute designs drift the same way?
One thing I don't think is understood is that air always flows around an object from one direction. When a parachute is descending, the air only flows past it from the direction that is is heading. There isn't also a second airflow from the side or horizontally parallel to the ground. If you stand still, you might feel a breeze hitting you from the left. But, if you start walking quickly, it will feel like the breeze is coming more from in front of you. You don't feel two separate breezes. You experience the vector product of the wind and the airflow you create when moving forward. So, as the parachute falls through the air, there is no wind pushing it on the side, there is just the flow of air around it from the direction that is falling.
When the wind changes, a parachute isn't hit on the side by a gust of wind. The parachute is falling, so the air is passing it from the same angle as it is descending. When the wind changes, the angle that the air flows around it will change. So, for an instant the cross section of the parchute exposed to the air stream will change. This would change the direction the the parachute is descending and, for a bit, the descent rare. If it reduces the drift, it will be because the rate of descent increases for a bit.
What you are saying here does not make any sense to me at all. Maybe I'm not getting it, or maybe you need to explain it better, or maybe it's wrong. OF COURSE, a parachute can be hit on the side by a gust of wind! And of course wind exerts a force on the chute when it hits it from the side. We are talking about chutes drifting in the wind, right? So I think we both agree that a parachute is affected by wind, and a chute does drift with the wind. In order for that to happen, the chute must respond to forces exerted by the wind.
Say, for example, a chute is falling in zero wind, it is going to fall straight down, agreed? Now say that as it is falling, there comes a gust of wind moving horizontally at 10 miles per hour relative to the ground. Can you tell me what you think is going to happen when that gust of wind comes through?
Here's what I think is going to happen. The parachute is going to experience a 10 mph wind blowing on it from the side. It's already descending through the air, so, like you said, the net flow of air around the parachute is not 2 aisrtreams, it's the sum of the two, but now there is a 10mph component that is coming from the side that wasn't there before. That 10 mph wind from the side is going to exert a force from the side and begin to accelerate the parachute to the side. As it accelerates to the side, the airflow coming from the side will start to diminish as the parachute starts to match the speed of the horizontal wind. Eventually the chute will catch up and match the speed of the wind, and it will no longer be accelerating and will no longer be experiencing a force of wind from the side. It will be in equilibrium, descending and also moving horizontally with the wind. Does that sound right?
So back to the different chute designs. I'm saying not all chute designs are going to react to the same 10 mph gust the same way. Some are going to present a different cross-sectional area to the gust than others. That means that the same 10 mph gust will exert a smaller force on the chute with the smaller cross section than it will exert on the one with the bigger cross section. And that means it will cause a smaller acceleration to the side. If the side gust of wind is maintained long enough, then both chutes will eventually come to equilibrium and will drift at 10 mph with the wind, but the one with the larger cross-section will match the wind speed faster, and the one with the smaller cross section will take longer to get up to speed. The smaller one will experience a smaller force but for a longer time, until it comes to equilibrium. By the time the smaller chute is up to speed, the larger one will have drifted further with the wind than the smaller one.
And that's just taking into consideration the cross-sectional area and not other design factors. Some kinds of chutes flutter and collapse a bit on the side when they are hit by a gust of wind. Others don't. Some may tilt up on the side when hit by a cross breeze and will really pick up speed quickly. Other won't. All of that and many more factors will determine how a chute drifts on a wind.
In any case, there is no way for a parachute to "know" which way or how fast the wind is blowing. So, there is no way for one design of an unguided parachute to drift less at the same rate of descent. If you need more evidence, as a pilot how they determine the wind speed and direction when in flight and consider how an unguided parachute could attempt that task.
The parachute does not have to "know" anything to be affected by changing wind currents. Two different non-sentient objects can react differently to outside forces without having to know anything.