I would rather the government (and its entities) be completely secular than to masquerade as though it cares about God and truly honoring him.
Whether God is supposedly "honored" in public doesn't really matter all that much. I would rather see a nation that ignored God altogether than a nation that pretended to honor him with its words while denying him with its actions. IMO, the latter is far more dangerous than the former, and it is a more serious insult to God.
Whether or not the US pays lip service to God, the fact of the matter remains that a significant portion of this nation is not righteous in God's eyes.
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Romans 2
9What shall we conclude then? Are we any better? Not at all! We have already made the charge that Jews and Gentiles alike are all under sin. 10As it is written:
"There is no one righteous, not even one;
11there is no one who understands,
no one who seeks God.
12All have turned away,
they have together become worthless;
there is no one who does good,
not even one."[c]
13"Their throats are open graves;
their tongues practice deceit."
"The poison of vipers is on their lips."
14"Their mouths are full of cursing and bitterness."
15"Their feet are swift to shed blood;
16ruin and misery mark their ways,
17and the way of peace they do not know."[g]
18"There is no fear of God before their eyes."
. . . .
22This righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference, 23for all have sinned and fall short of the glory of God, 24and are justified freely by his grace through the redemption that came by Christ Jesus.
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Going to church and honoring God in public doesn't make any difference. One is not saved by going to church (I know everyone here would agree). In the eyes of God, if you do not believe, you are condemned already (John 3:18).
I submit that while the culture of America seemed to be more "Christian" in the past, there isn't a whole lot of difference with respect to honoring God. People used to fake it, and now they just don't care. I personally respect an honest rejection more than a false acceptance.