Has all decency left the entire planet?

Alex, I think that your definition of “teachings” differs from mine. I suppose that, for example, the removal of what was previously a national motto “In God We Trust” (a motto for a country which was actually founded on Judeo-Christian principles), or a simple moment of silence to let anyone pray IF he wishes can be seen by the secularists or the cynics as a form of “teaching”. I disagree. I see no point in further debate on the subject since it is obvious we disagree on what does, in fact, contribute (please note that I say contribute to,  not “caused”)  to moral decline in a society. I feel I have explained myself fairly well on that point.

**** should not be part of public education in secular society. ****

Honest question: Why not? I have explained what I think is the harm in the removal. What exactly is it you think is the harm in not removing it?

Agree frogman , but in "God We Trust "was on our Currency  where
the true American God  is . Money .

Frogman, I disagre with a term 'in fact' in a context you have used it. 
But, let me explain my thoughts, aldo I am sure that you are quite familiar with everything I 've got to say.
With all due respect I am surprised that I have to write such things in year 2020 (why religious education or upbringing should remain private thing)

The state has power not based on divine law (jus divinum) but on social contract that transcends religious, religious and any other personal or particular interests.

The state is thus positioned wider and more general than any particularism, especially religious, in order to guarantee citizens neutrality,  so that every citizen  can address the state if certain groups threaten his existence and world view by imposing his particular belifs

According to the postmodern understanding of society, the religious community as well as all social associations not only have the right of political stance, it is indispensable for pluralism to be complete. But in order to maintain pluralism, the state must remain the sole guarantor of generality and neutrality, and its constitution a guarantor of abstractness so that no particularity or individuality is favored. The law (constitution) of the state,let us not forget, is not written on a case-by-case basis and can apply equally to everyone only if the state is not part of any particular association

Religious education in public school classrooms would impair the neutrality of the state.The students of 'other' confessions or agnostics might think that, in addition to the equal rights they enjoy, there are nevertheless those who are more desirable, or "more equal" than them.

Some society might be, religiously and culturally majority religious, but it is decisive that this fact has nothing to do with the notion of majority or the notion of state, which in a civic sense should ensure neutrality for those who are in the minority.

It is precisely in this symbolic example (absence of religious education or any other form of religious influence in public or 'official' institutions) that the importance of state neutrality is perceived, that is, the reason why it emerged as an abstract, impersonal power which, in its breadth, abstractness and generality, transcends particularisms, in this case religious, but also of any other.

Only if there are no particular features in such places, citizens of another confessions or non religious people can except the state (or school) as their own, as one that is not only for members of some particular confession. Citizenship is not related to confessional affiliation. Nationality and citizenship in the western tradition differ and are not conditioned by religious affiliation, which is why citizenship as a legal term is broader and more general than belonging to a nation or confession.

In simplified terms, this means that no matter how many citizens on the census declare themselves believers for any reason, state neutrality exists because of one citizen who does not declare himself so. Only then can one speak of the liberal-democratic character of the state, because the will of the individual is protected from the will and worldview of the overwhelming majority. 

One slight problem with what you say Alex . To a large degree what you say
is applicable ONLY in Denmark, Norway. Iceland ,Sweden, Finland and Canada .
To a lesser degree in Baltic lands .

What you say is pure fairly-tale in US which is a Republic and NOT a liberal -democratic anything..In Germany maybe 50/50 .In other large , powerful lands its dog eat dog . Biggest dogs are owned by richest people and those who serve them .

Schubert, allow me to correct you, it might be a surprise.
Also, many of following states are Republics too and all western countries are considered to be liberal democracys, in fact, here is the link

https://en.wikipedia.org/wiki/Liberal_democracy

In Europe, only Spain, Romania, Norway and Turkey have some sort of mandatory religious education.

In Norway such subject is called ’Christianity, religion and philosophy of life’ and it is going thru public discussions is it ’fair’ or not to be educated.

In Spain you might be excluded from such education if you bring the conformation that you are not religious, the rule which has seen objection as well.

In Austria, Italy, Germany, Poland, Portugal and in some ex Yugoslavian states, the pupils can attend such subjects at schools, but religious education is not mandatory, meaning that children can usually chose between religious or some sort of subject that teaches ethics (also not mandatory)

Belgium has the same model, but the classes are mandatory, one or another kind

Greece, Holland and Great Britain have different solution. The teachings about religion are included in some subjects which are not stricly religious

So, in Greece its called ’The history of religions’ , the Dutch have something that can be translated as ’Knowing of societys, with history of religion included and in Britain they learn about few different religions and its praxes

France, Hungary, Bulgaria and Czech republic have no religious education at schools at all.

The Switzerland have many different models, all above included.

In constitution of EU, there is no mention of religious roots or connections
.Is it a fairy tale for the US, I would not know, but its never too late to become your reality too