My dear friend you have to see things thru the window of dispensationalism. This section is talking about the people who survive the tribulation period who are unsaved. The Angels of God will remove them and the 1000 year reign of Christ will begin. All surviving individuals who are regenerated -by Faith in Christ- will only enter into the Kingdom. Read Daniel 12:11-12, Matthew 13:29, 30, 38-43, 46-50. That which offends will be removed.
Also, the trumpet is not even mentioned in Matt 24. I once also held that view. I encourage you to look thru it carefully and be objective. It is always well to challenge your belief to see if it stands the Biblical test. I have always done it and Almighty God has always lead me to the truth. Here is alink below that might be helpful
God Bless! (John 16:12-15)
http://www.middletownbiblechurch.org/dispen/dispensa.htm
Mathew 24:31--And he shall send his angles with a great sound of a trumpet, and they shall gather together his elect from the four winds, from one end of heaven to the other.
Sounds like a trumpet to me. His elect are the saved not the unsaved. Nowhere in Matthew 24 (or the other verses you cite) are the elect removed before the tribulation. There is one harvest.
All those "Left Behind" movies have left many with the mistaken impression that the elect will be removed before those days. Wishful thinking. Matthew 24:40,41 describe two working in a field where one is taken, the other is not. And two women at the mill, one is taken the other is not. Jesus says this will occur after the tribulation of those days. He describes no rapture before that time, an important event to not mention.
Matthew 24:21 says the tribulation will be unmistakable-- "For then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor everal shall be. And in Matthew 24:29 Jesus describes the day of Lord which will occur AFTER those days. If you're expecting a pre-tribulation rapture, you're going to be sorely disappointed.