In other words it is more likely due to converts to Catholicism who wished to continue worshiping their previous Gods at the same time who created a parallelism. The comparison which was then denounced from the pulpit from the very beginning as not being true. It's not to hard to see it happening however since in Asian countries there are many who do the same thing today or since local beliefs often tend to color religious ceremonies of Monotheistic practitioners in any country.
The earliest rapprochement of the births of Christ and the sun is in Cyprian, "De pasch. Comp.", xix, "O quam pr
æclare providentia ut illo die quo natus est Sol . . . nasceretur Christus." — "O, how wonderfully actedProvidence that on that day on which that Sun was born . . . Christ should be born."
In the fourth century, Chrysostom, "del Solst. Et Æquin." (II, p. 118, ed. 1588), says: "Sed et dominus noster nascitur mense decembris . . . VIII Kal. Ian. . . . Sed et Invicti Natalem appelant. Quis utique tam invictus nisi dominus noster? . . . Vel quod dicant Solis esse natalem, ipse est Sol iustitiæ." — "But Our Lord, too, is born in the month of December . . . the eight before the calends of January [25 December] . . ., But they call it the 'Birthday of the Unconquered'. Who indeed is so unconquered as Our Lord . . .? Or, if they say that it is the birthday of the Sun, He is the Sun of Justice."
Already Tertullian (Apol., 16; cf. Ad. Nat., I, 13; Orig. c. Cels., VIII, 67, etc) had to assert that Sol was not the Christians' God; Augustine (Tract xxxiv, in Joan. In P.L., XXXV, 1652) denounces the heretical identification of Christ with Sol.
Pope Leo I (Serm. xxxvii in nat. dom., VII, 4; xxii, II, 6 in P.L., LIV, 218 and 198) bitterly reproves solar survivals — Christians, on the very doorstep of the Apostles' basilica, turn to adore the rising sun. Sun-worship has bequeathed features to modern popular worship in Armenia, where Christians had once temporarily and externally conformed to the cult of the material sun (Cumont, op. cit., p. 356).