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

[True Federalist (진정한 연방 주의자)]

Potentially sacrilegious to be profaning God by implying that God can be wielded as a talisman to back up our money.  What our money needs is a copy editor, so that it reads: "In Gold We Trust".

[True Federalist (진정한 연방 주의자)]

Vindex, in Arabic, ﷲ has the same meaning as God, so open up any Arabic Bible and where an English Bible uses God, it will will typically have ﷲ as the chosen translation.  So much for your Bible explanation.

Of course, you are correct that in the original, Allah is never used, but neither is God, instead you'll find, יהוה , אֲדֹנָי. or the like.  and instead of I AM WHO I AM, you'll find אהיה אשר אהיה .

[True Federalist (진정한 연방 주의자)]

Vindex, in Arabic, ﷲ has the same meaning as God, so open up any Arabic Bible and where an English Bible uses God, it will will typically have ﷲ as the chosen translation.

The important thing is the term's meaning in English.

Which meaning Allah has in English depends on the speaker and context just as God does.  Some take God to mean the supreme deity of any religion, while others take it to mean God specifically in the Christian sense of God the Father.  Similarly, Allah can be viewed as the supreme deity of any religion, while others take it to mean Allah specifically in the Muslim sense of Allah, whose last prophet is Muhammad.

[True Federalist (진정한 연방 주의자)]

While speaking English? Even if that's true, the peculiarities of foreign dialects are beside the point. What matters is that Americans are not accustomed to using the term in this generic sense. Consider, e.g., Shorter Oxford English Dictionary (6th ed. 2007) (defining "Allah" exclusively as "[t]he name of God among Arabs and Muslims").

Note that usage includes Arab Christians.

[True Federalist (진정한 연방 주의자)]

If you think they are so irrelevant, Constitution can be amended.

What does that mean?

Presumably that he feels that it is better that changes to the Constitution and its interpretation occur via amendment that by judicial rulings.

[True Federalist (진정한 연방 주의자)]

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.

[True Federalist (진정한 연방 주의자)]

Because the meaning of language can only be understood properly in context and time is part of context.  This isn't a case like the Eighth Amendment where the class of cruel and unusual punishments can reasonable be argued to change over time.  The Eighth is concerned with preventing arbitrary and capricious punishments being handed out, not prohibiting a specific set of punishments. The establishment clause is specific and has no aspects that are mutable as society changes.

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?

I don't like the motto, but that's because I find it insipid, not because of any constitutional flaw it possesses.  Constitutionally, it has the same standing as annuit cœptis which has been one of three mottoes on the Great Seal of the United States since it was created in 1782 and which also has a non-doctrinal religious character.  The usual translation of the Latin into English is "He (God) has favored our undertakings."

[True Federalist (진정한 연방 주의자)]

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".

Also you're misconstruing the term "respecting" as it is clear from the context that the word is being used in its older sense equivalent to "concerning".  If one were to rewrite the establishment clause using terms that would be unambiguous in 21st century English, it would go: "Congress shall make no law concerning support of a particular religious organization, or prohibiting the free exercise of religion."  Having "In God We Trust" as the national motto violates neither restriction.