I agree that the first four appear to reference religious ideology more than the rest that reference morality and common sense. Of the remaining six, three really shouldn't be regulated by law:
5. Honor thy father and thy mother: that thy days may be long upon the land which the Lord thy God giveth thee.
7. Thou shalt not commit adultery.
10. Thou shalt not covet thy neighbor's house, thou shalt not covet thy neighbor's wife, nor his manservant, nor his maidservant, nor his ox, nor his ass, nor any thing that is thy neighbor's.
And the remaining three are indeed common ideas in law that are explicitly found in the Code of Hammurabi, which pre-dates the Old Testament:
6. Thou shalt not kill.
8. Thou shalt not steal.
9. Thou shalt not bear false witness against thy neighbor.
So out of these 10 Commandments, only three really have any business in secular law -- and they aren't original with the 10 Commandments anyhow, as they are recorded in human history before the establishment of the Old Testament.
"Honor thy father and thy mother" is the foundation for laws that give biological parents first claim on children.
It is also the basis by which parents are now subject to legal prosecution for their children's misbehavior.
This commandment *is* in secular law several ways, several places, and in contemporary times.
"Thou shalt not commit adultery"
This commandment *is* in secular law in a couple of different ways. First it is the foundation for the marriage principle. It is extremely important if it is violated, when considering divorce, and it has secular implications regarding reinforcement of the marriage-as-a-contract viewpoint of marriage. MORE...it is the foundation against statutory rape of the young and counsels wisdom for youth against disease.
"Thou shalt not covet..."
Would seem to create a "thought crime" if enforced in secular law. You can find it, nonetheless, in "hate crimes". It counsels wisdom, and oddly enough also lower taxes.
The 10 Commandments are the foundation of Law in Western Civilization...and will always be the root of law if it is banned.