Not to be picky, but...America was not created by a Christian society, nor were they seeking religious freedom. It was created by a small group of secular free thinkers who went to great lengths to separate Church from State in an effort to, in part, prevent the religious violence that had devastated England for the last several centuries.
Some of them were Christian, some were Deists, others were Theistic Rationalists.
'In God We trust' didn't appear on coins until 1864, and not on paper money until 1957.
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But yes, I agree with sentiment that there's no need for hyphenated citizenship, in name or ideology. The Statue of Liberty's "Give me your tired, your poor..." poem ("The New Colossus" by Emma Lazarus) is pretty clear.
But I also recognize that's not necessarily a mainstream opinion these days. And I'll leave it there to avoid slipping into politics.