Is having "In God We Trust" on money, buildings, etc. constitutional?

[WillK]

The first amendment states that congress shall make no law respecting the establishment of religion ... 

Actually the wording of the Constitution is "an establishment" not "the establishment", a subtle but i think very significant distinction.

[WillK]

Why amend the Constitution to ban something that is already unconstitutional?

I'm not quite sure how that is relevant to my point.
Let's look at the actual text of the establishment clause:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof

No particular church is receiving these dollars marked with a bland trite statement, so it is not an "establishment of religion" as the term would have been understood in 1787, nor is anyone required to use physical U.S. currency if they feel that having that phrase on their money violates their religious beliefs (or lack thereof) so the free exercise of religion is unimpaired.

But did Congress pass a law "respecting"  a religion?   If they passed a law specifying that a certain religious phrase be put on government documents, then I think a case can be made that they did respect a religion.

[WillK]

However, even assuming one were to interpret the clause as a total prohibition on any form of religious statement by the government, would that not in effect be establishing agnosticism as the national religious creed, thereby rendering such an interpretation self-contradictory?

No.  This is idiotic logic. 

[WillK]

But did Congress pass a law "respecting"  a religion?   If they passed a law specifying that a certain religious phrase be put on government documents, then I think a case can be made that they did respect a religion.

You're misinterpreting the literal meaning of the phrase.  It's "respecting an establishment of religion", not "respecting a religion".  No particular "establishment of religion" (i.e., religious organization) is involved with the phrase "In God We Trust".

Ok.  The phrase seems to me to be Christian in orgin and I tend to think of Christianity as an organized religion, but I suppose it is so fractured that only the sects of Christianity are religious organizations.

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No, I think I understood respecting correctly, since i understood it similarly to you.  I did make some edits to your rewrite.