Are the Ten Commandments Really “Judeo-Christian”?

Again and again we hear it: Remove the Ten Commandments from the walls of this public building, that establishment, or courthouse because The Ten Commandments are Judeo-Christian, and we insist upon (the imaginary) separation of church and state.
But are the Ten Commandments really meant for Judeo-Christians only?
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Let me quickly sum up The Ten Commandments:
Do not put anything between you and God and do not use His Name disrespectfully, take a day off to rest once a week, be respectful to your parents, do not murder anybody, be true to your spouse, do not steal, do not lie, and do not set your heart upon something that belongs to somebody else.
All things considered, these “Ten Commandments” appear to be quite appropriate in a courthouse.
So you out there who are “offended” by the presence of the Ten Commandments, the only conclusion I can draw is that it is fine with you if somebody steals your belongings, infidelity is no problem, you never appreciate a day to rest, murder is a good solution to any problem, and lying is just a normal part of every day life.
And what religion teaches its followers to put something between themselves and their deity? Everybody has a god– for example, it may be nature, money, or possessions. And nobody wants anything separating them from their chosen god, nor do they want anybody speaking disrespectfully of their god.
The practice of Islam is to cut off the hand of one who steals. If a woman is raped, the practice of Islam is to find her guilty of fornication and condemn her to a brutal death. And we all know what happens to anybody who the Muslims even perceive has disrespected their god, Allah, do we not?
In conclusion, The Ten Commandments are a code of good behavior telling us to behave decently toward each other in this world. Am I to conclude that only Judeo-Christians think this is a good idea?