Would early Christians find devotions to the saints akin to worship of the Roman Emperor? Is worship of the emperor akin to the worship of mary? (hyperdulia).
We should keep in mind that the RCC only considers an act to be worship if a sacrifice is made. So, for RCs, offering incense to the statue of the emperor would be worship. (Biblically though, worship can also be contrition, prayers etc.) I believe this is a distinction with no difference--many Christians were martyred for refusing to worship a being they certainly thought were lower than the Triune God.
For Lutherans, to worship is to receive the gifts God offers in the preaching of the word and in Holy Baptism, Holy Communion and absolution. So, for us any veneration in exchange for such blessings would be wrongful worship, which is due only to God.
Now, let us start with the Martyrdom of Polycarp.
“What harm is there in saying, Lord Cæsar, and in sacrificing, with the other ceremonies observed on such occasions, and so make sure of safety?”
Sacrifice was specifically requested. Thus, as a Christian, he could not offer this worship toward the Emperor.
“Have respect to your old age,” and other similar things, according to their custom, [such as], “Swear by the fortune of Cæsar; repent, and say, Away with the Atheists. hen Polycarp with solemn countenance looked upon the whole multitude of lawless heathen that were in the stadium, and waved his hand to them; and groaning and looking up to heaven he said, 'Away with the atheists.'”
No sacrifice, but a specific request to renounce the Christians--“Away with the Atheists”. Polycarp adroitly turned the "Away with the atheists" statement around, but he did not do so with swearing by Caesar, because that would be worship.
“Swear by the fortune of Cæsar,”
No sacrifice, no denunciation. In other words, no worship. It sounds like the proconsul was ready do compromise. For Lutherans, swearing by the fortune of Caesar constitutes worship, because to do so is to ask for a supernatural benefit from a mere man.
Now, though the emperors were called "gods", we should keep in mind that the actual term used was "divus" or "divine", a lesser state of deity, if you will. Hence, the emperor was not offered latraea. So, even the Roman Emperors were not worshiped in the same way a Christian would worship the Triune God, he was a lower order of being--similar to St. Mary and the other saints.
So, what does RC Marian devotion look like?
Another recommended Marian devotion is wearing the Brown Scapular of Our Lady of Mount Carmel. There are many Scapulars, all valuable, but this one is eminent among them. There is a very ancient tradition that St. Simon Stock, Superior of the Carmelite Order in England in 1251, after imploring the help of Our Lady, was favored with a vision in which she gave him the Scapular, saying: "This will be a privilege for you and for all Carmelites, that he who dies in this will not suffer eternal fire." The historical evidence for this vision is very impressive, and gives at least some degree of moral certitude that the vision really did take place. To gain this promise one must be enrolled in the Confraternity of the Scapular. Pope Pius XII, on the 700th anniversary of this vision, wrote to the Major Superiors of the Carmelites, clearly showing his belief in it: "For not with a light or passing matter are we here concerned, but with the obtaining of eternal life itself, which is the substance of the Promise of the Most Blessed Virgin which has been handed down to us."Source: http://www.ewtn.com/faith/Teachings/maryd7.htm
However, the Pope warned that the mere physical wearing of the Scapular is not enough: "May it be to them a sign of their Consecration to the Most Sacred Heart of the Immaculate Virgin, which in recent times we have so strongly recommended." If one then uses the Scapular as the outward sign of living such a Marian consecration, then faith in the fulfillment of the promise is well justified. In fact, Pope Pius XI said (Explorata res. Feb. 2, 1923): "Nor would he incur eternal death whom the Most Blessed virgin assists, especially at his last hour. This opinion of the Doctors of the Church, in harmony with the sentiments of the Christian people, and supported by the experience of all times, depends especially on this reason: the fact that the Sorrowful Virgin shared in the work of the Redemption with Jesus Christ." In other words, a solid Marian devotion is certain to bring one close to Jesus Christ, and so will assure one of reaching salvation, even if the vision to St. Simon Stock might not be authentic. Also, when Vatican II said that all things recommended by the Magisterium of the Church towards her should still be considered matters of great importance, the Scapular was clearly included, for numerous Popes have recommended it strongly.
From a Lutheran standpoint, this is worship--performing pilgrimage to carry out a change within us.
Clearly, one consecrates one's self to St. Mary, and receives a guarantee of salvation so long as one's devotion is true. Of course, I am aware that RCs believe this salvation actually comes from Jesus. My concern here though, is do discern how the RCs differentiate between the devotion to the vergin via the scapular, and merely swearing by the genius of one's ruler. Clearly neither is "worship" in the RC sense--nothing is sacrificed. However, Christians were willing to die in order to avoid a simple act of obeisance to the emperor, while similar devotion to St. Mary is encouraged. What, in the Imperial cult, made throwing incense in the name of the Emperor’s “genius” idolatry, while invoking Our Lady Mary to save us is not?