Of course, the Declaration of Independence does say this. But one must ask are men truly created equal? And if they are only equal before God and the Law but not as too innate heritable ability then does this not imply the Declaration has made a simple, empirical falsehood in claiming equality?
Of course they had Bibles. But God has been worshipped for thousands of years without anyone finding a political system that guaranteed unalienable political rights. The Bible, I remind you, does not mention Lockian social contracts or democracy. Indeed, I am looking forward to the Kindom of God.
America is a nation. The preamble to the Declaration of Independence is not law. The Constitution of the United States is law. Office holders, including military officers, swear an allegiance to the Constitution not the ideals of the Declaration.
IMHO, America is only half ideologically driven. The other half is a people with a history before the Declaration and a history until such time as God decides. The type of our government evolved out of our experience and the experience of generations past (including Great Britain)and is only a part of our endowment that includes religious, ethical, historical and unrecorded experiences as a people.
In a word, I don't think we are an ideology but a nation; hence, it does not surprise me that other nations have great difficulty accepting both or values and political system.
The context of "all men are created equal" in the Declaration was unalienable rights. Heritable ability is not an unalienable right.