The gospels seem to be peppered with demonic possessions that are nonchalantly noted by the author. Is there evidence that the ruling secular powers of the day acknowledged these as demonic possessions as well? Has a government acknowledged them afterwards?
Demonism and general belief in a spirit world are all interrelated. Surprisingly in Africa there is still an arguable case to say the secular government still admits the existence of potential demonic possession as it still has laws against witchcraft. In most other places 'secular' recognition of a spirit realm ended around the 1700s. For example in 1745 witchcraft was no longer a crime in England.
Every culture has a history of belief in ghosts and spirits. The outward phenomenon or behavior that would be potentially described by historical Christianity as 'demonic possession' is described by similar terms according to the form of religion the culture has. The question is therefore when did society make legal systems that no longer admitted the existence of a spiritual realm that could interact with the the physical realm. In other words when did governments truly become 'secular' in the modern atheistical, agnostic scientific sense?
The quickest and most accurate way to answer this difficult question is to see when laws against witchcraft ended. In most countries laws against witchcraft have ceased. However as Africa has had arguably the most extensive history of spiritism and apparent demonic possession, it seems that even today the laws are not fully repealed.
The legal system enacted in 1957 with respect to witchcraft is still in force and states:
The act criminalises a number of actions. The following two crimes, the most serious under the act, attract a fine of up to R400,000 or imprisonment for up to 10 years. Imputing to any other person the causing, by supernatural means, of any disease in or injury or damage to any person or thing, or naming or indicating any other person as a wizard
This does not directly answer the question in terms of demonism but I think you can see that when secular governments still believe that spirits can cause disease then they will usually believe is some sort of demonism also. Every culture has since this time people recorded history generally believed in a spirit world and some form of what we would call possession. Even in the modern secular era many civil servants and lawmakers will,personally have religious private beliefs. So the lack of belief is in some ways imaginary for the sake of separation between church and state. Usually only genuine atheists confidently deny an existence of a spirit world.