If there was widespread, open worship of the Greco-Roman pseudo-deities in modern America, evangelical Christians, if they were consistent with the rest of their legalism, would think that eating food offered (or "sacrificed") to idols or the pantheons is evil. Paul addresses this phenomenon in his own era as he writes in 1 Corinthians 8:4-8. He does not have to mention Deuteronomy 4:2 to be consistent with Yahweh's command to not add to his instructions. There is no condemnation of eating such a thing, even if the pagan philosophies and practices associated with the sacrifice of food to idols are invalid.
What might seem like an egregious yielding to paganism is something that Paul, as any Christian theonomist who understands Mosaic Law would realize about this matter, recognizes as permissible: eating meat sacrificed to idols is not problematic if one is not ideologically allegiant to paganism. Meat is just meat, and offering food to nonexistent or lesser spiritual entities (lesser than Yahweh) does not mean a person is worshipping or entering an agreement with them. To participate in the consumption of such meat is not to participate in any sort of psychological or outward act of devotion to any pagan being.
Paul affirms that idols have no power because they are mere objects (1 Corinthians 8:4). He goes so far as to admit that even if there are or were such pagan entities, Yahweh would still be greater and more philosophically central, ultimately because he is the uncaused cause and the one whose nature grounds moral obligation altogether (8:5-6). Yahweh and Christ are the beings Paul advocates for submission to because they would have authority beyond that of the pagan pantheons, which contain many so-called gods or goddesses who are created beings even according to their own worldviews and stories. Without elaborating extensively, Paul touches upon this by mentioning how God and Jesus (which he correctly distinguishes as separate metaphysical beings) created the world and by extension its people and animals (8:6).
Of all the things supposedly repealed or nullified by Jesus in Mosaic Law, the dietary laws are among the only things that either by logical necessity are not universal obligations according to Christianity or that are more ambiguous as to whether they are obligatory. The dietary laws of the Torah, however, only prohibited eating certain kinds of animals not according to whether their flesh had been sacrificed to idols or pagan pantheons, but based on criteria such as whether a creature of the water does not have fins and scales (Leviticus 11:9-12). Even under the full dietary restrictions of Mosaic Law, it is not the association of the food with pagan worship that is the basis for abstaining from it.
As strange as it might seem to some, as with how many other controversial things are Biblically nonsinful, eating meat that has literally been offered to pagan pseudo-deities or the physical images depicting them is not immoral according to Mosaic Law, the only moral revelation in the Bible that is direct, holistic, and precise all at once on a consistent basis. Paul acknowledges that this is not ultimately problematic even if it offends or terrifies some Christians. If a person wishes to eat or do any other such nonsinful thing, they are morally free to do so. If a person wishes to not eat or not participate in any other such nonsinful thing, they are morally free to not partake.