The Mishna says that 3 days before and after a holiday of avoda zara one is not allowed to have business dealings with goyim because they will be thankful to the avoda zara for their success, so the Jew is indirectly causing worship of avoda zarah. Tosafos asks how we can be lenient about this nowadays to even do business with goyim on their holidays? At first Tosafos suggest that it is permitted to prevent "eivah" - animosity and to prevent inciting tensions between Jews and goyim, but this is not sufficient because it wouldn't explain how we can take the initiative to collect from them and do business, since abstention from these activities wouldn't lead to "eivah". From the fact that we allow something like this for the purpose of eiva, indicates that the entire prohibition is only d'rabonon because we aren't matir issurei d'oraysa to prevent animosity. Rav Moshe (Igros Moshe O.C. 1:71) points out that even if the Jew will definitely cause them to worship avoda zara it isn't considered an issur d'oraysa since he is not intending to do it for this purpose and qualifies as a davar sh'eino mis'kavein.
Tosafos offers 3 approaches: 1. Goyim nowadays aren't so observant and don't attribute their success to avoda zara so it doesn't lead to worship of a.z. 2. Based on the Yerushalmi that allows it for a goy who you have a relationship with to be "machnif" him. This answer of Tosafos seems to be based on the eivah approach but even permits actively doing things to improve the relationship with goyim. 3. Rabbeinu Tam has another approach to the sugya where he explains that only providing animals for sacrifice is forbidden, but anything else is permitted.
The Meiri explains that the issur only applies to goyim who worship the celestial beings, but no longer applies nowadays. It is unclear if the Meiri is writing this for the censors or if he honestly held that this would not apply to the religions of our days i.e. islam and christianity.