“The authorities knew that Peter was a leader of the Church, and the Church, under Roman law, was considered organized atheism. (The worship of any gods other than the Roman was considered atheism.) Peter would do himself, not to mention those with him, no service by advertising his presence in the capital—”
That is wrong. With the edict of Gallio at Corinth (Acts 18:14-14) Christianity was declared to be just another religion and in fact prospered under Caludius and Nero until the fire at Rome. That is one of the reasons for Paul’s admonition to the churches at Rome to be subject to “higher powers” so as not to disturb the peace as had the Jews under Claudius that led to their exile in 49 A.D..
Excellent observation