Looking for legal advice on preventing theft by high status respectable neighbors

In smaller towns and cities, high status respectable neigbors are criminally trespassing on the house of the domain investor and robbing whatever they wish. These neigbors are extremely religious and spend hours daily, reciting their prayers, yet they do not have any morals and will ruthlessly rob from neigbors who are new to city or town or are not well connected.
The robbed items are prominently displayed in the house of the robber neighbor.
Would also like to find out the legal issues involved in publishing photos of the robbed items in the neighbors houses, whether the neighbor can take legal action if a photo of one or more robbed items in his house is displayed online.
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