Why do most Christians seemingly not mind swearing on the Bible in light of Matthew 5:33-37?

The requirement to swear on the Bible, is in no way contrary to those things said by Jesus. If we take a closer look at the Scriptures sited we see that what Jesus is siting; are all things other than the Commandments of God.

Quoted from Peter Gusic's commentary of the whole Bible:

Matthew 5:33 through 37 KJV Jesus interprets the law concerning oaths. “Again you have heard that it was said to those of old, ‘You shall not swear falsely, but shall perform your oaths to the Lord.’ But I say to you, do not swear at all: neither by heaven, for it is God’s throne; nor by the earth, for it is His footstool; nor by Jerusalem, for it is the city of the great King. Nor shall you swear by your head, because you cannot make one hair white or black. But let your ‘Yes’ be ‘Yes,’ and your ‘No,’ ‘No.’ For whatever is more than these is from the evil one.” a. You have heard that it was said to those of old, “You shall not swear falsely”: The scribes and Pharisees had twisted the law You shall not take the name of the Lord your God in vain (Exo_20:7) to permit taking virtually every other name in a false oath. b. Do not swear at all: Jesus reminds us that God is part of every oath anyway; if you swear by heaven, earth, Jerusalem, or even your head, you swear by God - and your oath must be honored. c. But let your “Yes” be “Yes”: Having to swear or make oaths betrays the weakness of your word. It demonstrates that there is not enough weight in your own character to confirm your words. How much better it is to let your “Yes” be “Yes” and “No” be “No.”

When you swear on the Bible, you are in fact swearing that you are bound by God to honor your Christian relationship with the creator God; and not by any other thing, not any representation of God. Other forms of swearing are not an allegiance with God the creator, and thus the statement that you should not swear falsely.

The admonition to let your yes be yes and your no be no, is there for you, that you must take your obligation to do as you have said; is your commitment directly to God.

The key to understanding the passage is in the words: "Let your yes be yes, and your no, no." "Swear not at all," isn't a abolishment of all forms of oaths or swearing, but rather a command for Christians to be honest, and to create a society in which 'I swear!' should not be necessary. Say the truth; say what you mean.

The instruction not to swear an oath using God's name, throne, altar, etc. from the text is an injunction against invoking Him in order to add more gravity or credibility to what is being said.

It comes in the context of Jesus taking many of the commandments of God (no murder, no adultery,...) and stripping away outward obedience to reveal that conformity at the level of intent is required.

“Again you have heard that it was said to those of old, ‘You shall not swear falsely, but shall perform to the Lord what you have sworn.’ But I say to you, Do not take an oath at all, either by heaven, for it is the throne of God, or by the earth, for it is his footstool, or by Jerusalem, for it is the city of the great King. And do not take an oath by your head, for you cannot make one hair white or black. Let what you say be simply ‘Yes’ or ‘No’; anything more than this comes from evil. - Matthew 5:33-37

It is like saying, "This time I'm really not going to lie, I swear to God!", whereas God's command is to bear no false witness at all, ever. It is a very haughty spirit that compels a sinner to publicly promise God that His commands will not be broken, this is why Jesus says that anything else but yes and no comes from evil.

That being said, the legal requirement to make some kind of affirmation in a courtroom can be seen as simply an obedient participation in the civil process and need not represent a departure from Jesus' words. At the end of the day the decision to swear upon the Bible in court or request a secular affirmation instead must remain in the realm of personal conscience.