Something else about the people following Jesus is noted: they are “sinners” – ἁμαρτωλοὶ (hamartolos), which is a word used to describe “Gentiles”, or non-Jews. So who were the “sinners” that the Pharisee scribes were worried about? Greeks, mostly, but also Romans in general. Remember that the primary division in Judean politics at the time was the degree to which foreign influence was permitted, between Saduccees advocating full adoption of Greek ideals to Zealots violently rejecting Greek or Roman influence, Pharisees were in the middle, holding to traditional ideals, but doing deals with the Romans under the table. Being “Jewish enough” was a social problem they had managed since Alexander.
This is the gist of verse 16: how could Jesus be an authority for Jews if he’s not Jewish enough? Pharisee scribes were very concerned with issues of authority and sensitive to complaints that they weren’t appropriately traditional. It’s clear that Jesus has been in cahoots with the Pharisees at the very least up until this point. Here, the scribes put voice to a common complaint, so this isn’t something specific to Jesus.
It was a big deal for Romans to eat together, and to see Jesus consorting with Romans, like a rich, powerful Roman would, was a specific kind of propaganda. This guy wasn’t tied to the other political groups in Judea, but they were all beholden to him, anyway. He had Imperial Authority and was Very Roman, very rich, and very powerful. The fact that it would upset the Judean politics was really just icing on the cake.