Will the rapture cause airliners to crash all over and car wrecks everywhere?

No, the rapture will not cause airliners to crash all over and car wrecks everywhere. It is a quiet disappearance, and because there are not that many true believers, there might be one airliner go down somewhere, but not multitudes.

Les explains that the rapture is not a scene of cataclysmic judgment or the wrath of God falling all around; instead, it is a quiet disappearance. He warns against believing cartoons that show airliners going down all over and car wreck after car wreck. He points out that there are not going to be that many believers on the road, and there are just not that many true believers who will be gone. There might be one airliner go down somewhere, but not multitudes of them. Paul teaches that the Lord Himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God; the dead in Christ shall rise first, and then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air. This is comfort, not widespread destruction.

1 Thessalonians 4:15

For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep.

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Is the Rapture a quiet disappearance or a time of wrath and judgment?

The catching up of believers is presented as a quiet disappearance, not cataclysmic judgment. Scripture describes the Lord descending with a shout, the dead in Christ rising first, and living believers caught up to meet Him in the air. The passage contains no wrath of God falling, only a sudden, quiet removal.