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Of course, the fingers of the priest are consecrated with holy oil during the ordination and are anointed. This difference must be stressed; the priest acts in the person of Christ through the sacrament of ordination. Only in extraordinary cases, such as the persecution of the Church or in the underground Church, were lay people allowed to touch the Holy Sacrament, to bring it to prisoners or dying people, and to expose the Blessed Sacrament for adoration.
In my time during the Soviet era, there were no priests, or they came very rarely during the year. So this happened, but not in the presence of a priest or under normal circumstances. Therefore, directly touching the Holy Host is a privilege of the priest because he is ordained and his fingers are anointed.
But I repeat, this must truly be an extraordinary case when there is no priest at all or only very rarely, as during times of persecution. Today, in the Western world, there is usually no persecution. There are even priests who can come more frequently than twice a year, as in our case during the Soviet era. This is the difference.