A Deist, who believes in a higher power, can accept the importance of all religions and simply believes in a God. Jesus and christianity had not yet been born.
We must draw the line somewhere. I choose to draw the line here, otherwise how much further can we go with this parsing of meanings and intents.
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.