There was a discussion years ago that covered the issue in-depth - if
going here or going here to a thread known as
Pesach...Something to Think About.
As it concerns understanding how St. John Chrysostom was addressing others who in the name of Judaism, tried to speak against Jesus since there was competition between the rabbis not believing in Yeshua/Jesus coverting people and the Christians converting others. It was never the ideology of the early believers that being strongly attached to Jewish culture (as a Jewish Christian) was ever wrong - or that believing in Christ meant forsaking all things the Jewish people did with God's guidance.
The Early Church Fathers were highly connected to the Jewish culture (including St. John) and we have address that for what it is if we're to be accurate...
Being Jewish myself (on the West Indian side of my family via my Great-grandfather's mother who had Rabbi as a grandfather), of course the issue hits home for me whenever seeing people throw out a lot of things in ignorance by confusing an insistence on all Gentiles acting "Jewish" (despite the diversity within the Jewish world as to what it means to be Jewish) with Jewish culture/practices the Apostles continued alongside other Hebrew Christians. Jesus himself had sharp terms for others in his own ethnic group who did not support the Gospel and other Jews have long pointed out that reality - but where it is said that one cannot honor their own culture if/when they are Jewish, it is indeed anti-Semitic. It is also unfortunate since people who are Jewish have long pointed out where they have called out others in the non-Christian Jewish world for ignoring Christ and yet have to deal with things from other Christians having no real understanding of Jewish culture or what the Church Fathers were actually standing against.
The most Jewish thing you can ever do is believe Jesus is the Messiah and there will never be escaping any kind of roots/the need for understanding intellectually how the faith was developed if wanting to be honest......

Christianity itself was considered a sect of Judaism - and that was well understood within the Early Church when addressing the fact that it was never about being against all things "Judaism" but rather a TYPE of Judaism since the Followers of the way were the inheritors to what Judaism was meant to be at the arrival of Christ (Acts 24:14). Of course there were greater divides between what Followers of the Way believed (Both Jew and Gentile ) and normative Judaism from which it sprung - and as it turns out, the strain of Judaism that existed/persecuted other Christians was actually what Christ and the Prophets spoke against when speaking of what God's true Israel would face in opposition to others claiming to represent His Nation and yet going against His Ways.
So the issue is not as "black and white" as it seems a lot of people make it to be - several other leaders within Orthodoxy have mentioned that before AND it takes a lot of time and understanding to fully grasp the situation.
That said, here are some good resources if wanting more research/study on your own time:
I'd encourage anyone wanting to investigate Orthodoxy's perspective on Jews to begin with understanding the roots of Orthodox worship/practice from a Jewish perspective.
Fr. James Bernstein is one of the most insightful minds on the issue and I've always appreciated his setting the record straight: