The first problem is to properly define religion. Not all religions worship deities. Buddhism, which is considered a major world religion has no deities, yet it is called a religion. Buddha was a precocious young man who used his mind and self observation to develop a philosophy and techniques, to achieve enlightenment. Therefore, a connection to deities, by itself, is not enough to infer all forms of religious propaganda. There is another kind of religious propaganda that is not as obvious as deities.
The problem is atheism has defined religion in a way that exempts itself. Their standard would not consider Buddhism a religion since this religion lacks deities. The Buddhists are happy to call this a religion and they should know better.
Atheism is the mirror image of Buddhism, in the sense atheism is about humans using the extroversion of science to evolve humanity, while Buddhism is about humans using introspection to evolve humanity. Both are based on humans activity to achieve higher states of knowledge and enlightenment. There are no deities involved, although some will worship those who take their respective techniques to the upper level; Buddha, Einstein, Darwin,etc.
One such non deity example of religious propaganda, that comes to mind, is the idea of utopian Socialism. Socialism has a connection to the teachings of Jesus. But beyond that, If you look at history, socialism does not turn out as well as the utopian fantasy that is always sales pitched. The sales pitch creates a paradise illusion but it never ends that way in reality.
This fantasy propaganda, in the light of hard data that says otherwise, would rank as a type of religious propaganda, since even atheism broadly defines religion as imaginary. Socialism is more in the mold of a religion without deities, where humans get to play God; Stalin and Castro, pillaging the wealth and power of their socialist nation, until they have the control over life and death.
The left wing religious propaganda about Trump being an incarnation of Hitler is a type of reincarnation religious propaganda. This and other types of religious propaganda has turned Trump into a type of fairly tale character, who symbolizes all that is wrong and evil with humans. This is not even rational, which may be another sign of religious propaganda.
The only reason this religious propaganda is being left alone is the Supreme Court once ruled that freedom of the press could not be hindered by litigation, and that public figures had to take even lies and slander with no way to appeal beyond public opinion. The press used to self censor and set limits, so this worked out. However, ever since Trump won, self censor was thrown out, knowing, even religious propaganda; fairy tales, would be protected under the statute. This freedom to speak, lies and religious fantasy propaganda, has misinformed the less than rational, like a sermon from a quick talking evangelist.
This statute may need to change in the near future, so subtle non-deity, religious propaganda, by the press, will be subject to liable and slander suits, unless they make it clear this is unsubstantiated fantasy or opinion. CNN may have to have post a large disclaimer, for 10 seconds, before each show, saying the following is for entertainment purposes only, and should not be taken seriously. This may head off the lawyers since it warns of religious propaganda; fantasy sold as authority.