Why does in god we trust not violate the constitution?

[FBaggins]

30. Because the constitution was in no sense anti-religious

You can't read "no law establishing" without the "free exercise" part of the clause and then just imagine what you think it means.

So many people had come here because they couldn't worship as they desired in their home countries - because those countries had state religions and often persecuted anyone who was not part of those "established" religions. So the founders intentionally created a union designed to avoid establishing a national religion. But nowhere did they say that religion in general could not be part of public life. They were clearly asking themselves what would allow the most "free exercise" for a pluralistic country... and clearly settled on keeping the federal government from picking a winning church/denomination.

Note that, at the time, they had no trouble with state religions. Nor did they have trouble with even federal statements of religiousness. Your reading of their intent cannot be correct or else the men who wrote it would not have allowed prayer in opening congressional sessions. You're faced with asking yourself "why didn't someone stand up at that first prayer and say 'um... guys? Didn't we just say that we couldn't do that???"