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.

Les explains that this catching up is not the Lord coming to Mount Olives and standing there, nor is it cataclysmic judgment or the wrath of God falling all around. Instead, he says there will be a quiet disappearance. He warns against popular cartoons of multitudes of airliners going down and car wreck after car wreck, noting there will not be that many true believers gone. He also points out that Paul includes believers with his own experience in chapter 4, using the pronouns “we” and “you,” and then directs attention to chapter 5 to watch the difference in language.

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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What will the rapture be like—will it involve judgment and wrath or a quiet disappearance?

The rapture is described as the Lord descending from heaven with a shout, the voice of the archangel, and the trump of God; the dead in Christ rise first, then living believers are caught up together to meet the Lord in the air. It is not cataclysmic judgment or God's wrath, but a quiet disappearance.

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.