Hi, David Toklikishvili,
"For critics, however, hosting a wedding ceremony with a controversial guest list evoked Georgians' familiar and uneasy feeling of having their country reduced to a place of food and entertainment by its northern neighbor."
The source: https://eurasianet.org/wedding...hter-riles-georgians
To me the sentence can be understood so as if Georgians wanted and caused their country to be reduced to a place of food and entertainment by its northern neighbor, whereas the writer apparently means that this has happened so against their will.
"Having" is not causative in that sentence, but existential.
Under 18.53 on page 1413 of Quirk's A Comprehensive Grammar of the English Language, we can read that these constructions can be interpreted as causative (with the subject having an agentive role) or existential (with the subject having an affected role):
He had a book stolen. [= A book was stolen from him]
She has had some poems published. [= Some poems (of hers) have been published]
In all these instances, the subject of have could be 'affected', but in some it could equally be agentive:
She has had some poems published. [= She has caused some poems (of her own or by someone else) to be published]
Context and the verb involved will determine whether the subject caused or merely experienced the action, respectively being agentive or affected. With a verb like "steal," it is clear that the subject did not want the action to occur. In He had a book stolen, "had" can only be existential.
In the sentence you quoted, the adjective "uneasy" suggests that "having their country reduced to a place of food and entertainment" was an undesired result (besides, no one in their right mind can want their country to be only considered as a place for recreational purposes). Therefore, "Georgians" is an affected, not an agentive subject, there.