The first thing we see about what is under dispute here is a thing called the "custom of Moses." This word custom is our word basically, ethos. You have heard about like a society, societal ethos or the ethos of a certain group or even an individual or a small group of individuals. And this word ethos means a custom or a tradition. In our own language, in our own usage, and this is consistent with the usage in Greek, ethos is the characteristic spirit, beliefs, and aspirations of a community, a culture, or an era. We can further define it that ethos is a code word for the laws, rituals, and traditions of a particular society or a particular people.
And so here in chapter 15, verse 1, by them saying the custom of Moses, what they are actually using is a code phrase for the laws, rituals, and traditions of Judaism. Not God's, not the Torah, not the Bible, not Scripture, but this is a code phrase for the laws, rituals, and traditions of their religion, Judaism.
In large part this refers to what became Jewish halaka. The whole body of Jewish teaching, legislation, and practices that proceeded from—listen to this—interpretation and reinterpretation of the Bible's laws; it is distinguished from God's written Word as the oral law or sometimes it is referred to as the traditions of the elders. Specifically, it implies all the nitpicky rules and regulations that had accumulated in the Jewish religion over the centuries since they had returned from Babylon. And those things had become customary—custom-ary—traditional for Jews to observe as part of their religious culture.