Here are some quotes that show that the earliest believers followed the Feast Days..
John Chrysostom said, "The festivals of the .. Jews are soon to march upon us one after the other and in quick succession: the feast of Trumpets, the feast of Tabernacles, the fasts. There are many in our ranks who say they think as we do. "
When, it says, the day of Pentecost was fully come: that is, when at the Pentecost, while about it, in short. For it was essential that the present events likewise should take place during the feast, that those who had witnessed the crucifixion of Christ, might also behold these...And, it says, there were dwelling at Jerusalem Jews, devout men. The fact of their dwelling there was a sign of piety: that being of so many nations they should have left country, and home, and relations, and be abiding there...for it was Pentecost. (Chrysostom J. The homilies of S. John Chrysostom, Archbishop of Constantinople: on the Acts of the Apostles, Volume 1, Homily IV
St. Jerome (PL 25, 1529 & 1536-7) speaking of how the believers celebrated the Feast of Tabernacles
tells us that they gave the feast a millenarian significance
Eusebius recorded that Polycrates of Ephesus, around 195 A.D. wrote the following to the Roman Bishop Victor who, as the previous writing showed, wanted all who professed Christ to change Passover from the 14th of Nisan to Sunday:
We observe the exact day; neither adding, nor taking away. For in Asia also great lights have fallen asleep, which shall rise again on the day of the Lords coming, when he shall come with glory from heaven, and shall seek out all the saints. Among these are Philip, one of the twelve apostles, who fell asleep in Hierapolis; and his two aged virgin daughters, and another daughter, who lived in the Holy Spirit and now rests at Ephesus; and, moreover, John, who was both a witness and a teacher, who reclined upon the bosom of the Lord, and, being a priest, wore the sacerdotal plate. He fell asleep at Ephesus. And Polycarp in Smyrna, who was a bishop and martyr; and Thraseas, bishop and martyr from Eumenia, who fell asleep in Smyrna. Why need I mention the bishop and martyr Sagaris who fell asleep in Laodicea, or the blessed Papirius, or Melito, the Eunuch who lived altogether in the Holy Spirit, and who lies in Sardis, awaiting the episcopate from heaven, when he shall rise from the dead? All these observed the fourteenth day of the passover according to the Gospel, deviating in no respect, but following the rule of faith. And I also, Polycrates, the least of you all, do according to the tradition of my relatives, some of whom I have closely followed. For seven of my relatives were bishops; and I am the eighth. And my relatives always observed the day when the people put away the leaven. I, therefore, brethren, who have lived sixty-five years in the Lord, and have met with the brethren throughout the world, and have gone through every Holy Scripture, am not affrighted by terrifying words. For those greater than I have said We ought to obey God rather than man (Eusebius. Church History, Book V, Chapter 24.
Irenaeus records this about Passover in reference to Polycarp: And when the blessed Polycarp was sojourning in Rome in the time of Anicetus, although a slight controversy had arisen among them as to certain other points
For neither could Anicetus persuade Polycarp to forego the observance [in his own way], inasmuch as these things had been always observed by John the disciple of our Lord, and by other apostles with whom he had been conversant; nor, on the other hand, could Polycarp succeed in persuading Anicetus to keep [the observance in his way], for he maintained that he was bound to adhere to the usage of the presbyters who preceded him.
Apollinaris, wrote: "There are, then, some who through ignorance raise disputes about these things (though their conduct is pardonable: for ignorance is no subject for blame it rather needs further instruction
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The fourteenth day, the true Passover of the Lord; the great sacrifice, the Son of God instead of the lamb, who was bound, who bound the strong, and who was judged, though Judge of living and dead, and who was delivered into the hands of sinners to be crucified, who was lifted up on the horns of the unicorn, and who was pierced in His holy side, who poured forth from His side the two purifying elements, water and blood, word and spirit, and who was buried on the day of the passover, the stone being placed upon the tomb" From the Book Concerning Passover