Before we can answer this question, we first need to define what religion is. Not all religions worship deities. For example, Buddhism does not have deities, yet it is one of the largest religions in the world. Religions can be more about philosophy and lifestyle without any mention of God.
One may ask is PC is form of religion that has no deities? One cannot use certain godless names in vane. Is feminism a form of religion? Is man made global warming and environmentalism religious sects that all worship mother earth? Are political parties forms of religions? Politics and religion can trigger the same levels of excitement or combativeness in their flock. What about all the fake news worship services against Trump. Is that a form of religion since it teaches things that are imaginary to its worshipers who then blindly believe?
The left tends to define religion as anything associated with Christianity. That is the only religion they seem to target. This output affect sort of tells you their definition of religion. What can be done to Christianity would be called a hate crime for other religions. There is unspoken definition of religion that is too narrow and self serving. There is no big first 1st Amendment push against Muslims. If anything there is state run accommodation. Is this a break down in the separation of church and state, based on the leftist definition of religion? Or is that how the state should respect all religions?
The definition of religion needs to be clarified so we don't leave anyone out. A better way may be to define religion based on the affect on the individual instead of cause. The cause may or may not have deities, but the affect will often be very similar. If you met a devout Buddhist or Christian one can see their faith in their eyes even though one has deities and the other not. Reg output affect can be induced in many ways.
How is the output affect of a preacher teaching of heavenly paradise any different from a socialist painting the idealist picture of a socialist utopia that never seems to fully exist? Both are wishful places and both can make the audience feel good and can even motivate the audience along lines of prescribed behavior.
Back in the time of Rome, various human collective expressions from agriculture to war, had a god or goddess associated with it. If you were in the military this had the patron God, Mars. The difference today is we take away Mars; deity, but nothing else really changes in terms of the philosophy of the warrior. The output affect is still the same. Adding or taking away a deity is not a good litmus test. Separation of church and state allows for all these differences, which is why it is close to free speech, which can become political; non-deity religion.
One has to bear in mind that the state has an army and police, it can make laws, it has jails, it can tax, all backed by force. There is no religion, regardless of definition, that has this much power. Religions cannot form an army, their laws and taxes; tithes, are all voluntary. The state is the big dog and religion the little dog. The big dog does not need to protect itself from the little dog who has no teeth. Separation is there to keep the big dog on the leash, since he is all the big teeth.