Upvote:3
While we have only fragments of Polycarp, we do know that both Irenaeus, who heard him, and knew his successor bishops in his own day, accepted the Gospel of John.
He writes of his own having seen Polycarp when he was younger:
Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the Church in Smyrna, whom I also saw in my early youth, for he tarried a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom, departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true. To these things all the Asiatic Churches testify, as do also those men who have succeeded Polycarp down to the present timeβa man who was of much greater weight, and a more steadfast witness of truth, than Valentinus, and Marcion, and the rest of the heretics. ...
(Against Heresies, Book III, Chapter 3; 4)
And on how many Gospels they are - note how fundamental the Gospels are, according to Irenaeus, and thus the successor bishops of Polycarp (whom he nowhere accuses of rank heresy for rejecting any thereof):
... It is not possible that the Gospels can be either more or fewer in number than they are.
... And therefore the Gospels are in accord with these things, among which Christ Jesus is seated. For that according to John relates His original, effectual, and glorious generation from the Father, thus declaring, "In the beginning was the Word"
... But that according to Luke, taking up [His] priestly character ...
... Matthew, again, relates His generation as a man, saying, "The book of the generation of Jesus Christ, the son of David, the son of Abraham" ... This, then, is the Gospel of His humanity ...
... Mark, on the other hand, commences with [a reference to] the prophetical spirit coming down from on high to men...
For the living creatures are quadriform, and the Gospel is quadriform. ... These things being so, all who destroy the form of the Gospel are vain, unlearned, and also audacious; those, that is, who represent the aspects of the Gospel as being either more in number than as aforesaid, or, on the other hand, fewer. The former class [do so], that they may seem to have discovered more than is of the truth; the latter, that they may set the dispensations of God aside. ... But that these Gospels alone are true and reliable, and admit neither an increase nor diminution of the aforesaid number ...
(Against Heresies, Book III, Chapter 11; 8-9)
It's not possible that early Christians were divided on the core Scriptures that are the Gospels, and no mention is ever made of there being a dispute among Christians on the same. Only blatant heretics who are marked by their novelty or disagreement with the entire church spread across the world, showing their unorthodoxy.
As for the celebration of Easter and issues regarding the harmonization of the Gospels, these are subjective, and shouldn't be the basis for accepting or rejecting a Gospel. In fact, if Gospel's aren't handed on by tradition, then they become victim to judgement by anyone, and anyone and everyone determines which Gospels suit his interpretation and taste.