Yes, there absolutely is something wrong with it. "Muslim nations" have Islamic policies. Do you think any unbeliever is going to look at that and think we promote religious freedoms for all of our people? We can't separate "Christian nation" and outlawing all other religions in the minds of our citizens because of all the crap Muslim nations have done to Christians.
Nor should we. Islam is from Satan, and Muhammad brought nothing new that was good. (Emperor Palaeologos and Pope Benedict were right.)
We should still remember, however, the historical fact that it was the
Christian Kingdom of Axum (modern day Ethiopia/Eritrea) that first offered shelter to the Muslim migrants from Arabia, in Muhammad's own day. Did that change the religious character of the kingdom? According to some later Muslim liars/proselytizers, yes (in their tradition, he converted to Islam); according to
actual history as documented at the time, no.
So we can still allow the pagan to live in a Christian society without having to separate our religion out in this way, but no believer in a non-Christian faith therefore has some kind of right to make the society into something it isn't. All countries are God's because God is the Pantocrator (ruler over all); not because we declare them to be this or that. A 'Christian' society can very quickly become something else by demographic shift (we are seeing this now in the West, obviously), but this only happens when the majority (who are still Christian in the United States, anyway) don't vote as though they actually believe that their religion is true, but instead on the basis of not hurting their areligious, or Jewish, or Muslim, or whatever friends' feelings or something.
Because Christians were the people being prosecuted for heresy. If they were Jews, American would have been based on freedom for Jews.
What? America wasn't founded on religious freedom for Christian heretics. The Puritan pilgrims (who I
guess would've been heretics relative to the Church of England, maybe? I don't know) didn't found America; they just landed there. The founding fathers (signers of the constitution, etc.) were some Christians, and some generic 'deists' who were specifically anti-Christianity (see, e.g., Jefferson's Bible, where he cut out all the bits that pointed to Jesus' divinity that he didn't like/agree with). Probably because of that mix, they set up a society in which either view would be tolerated, but none would be promoted. But it's not like they said "We hold these truths to be self-evident; Gnosticism/Arianism/Monothelitism/Monophysitism/Adoptionism/Judaizing/etc. are all okay!" That would be a bit close to seeming to endorse particular religious views, wouldn't it?
Cf. the constitutions of the majority of Islamic nations, which specify Islam as the state religion, never to be contradicted, and some which go further and specify that Islamic Shar'ia is to be the source of legislation and never to be contradicted by any other law, etc. Those are positive affirmations of a kind that is not found in the U.S. constitution or bill of rights.