Avodah Zarah, Chapter 1, Mishnah 2. This mishnah picks up where the previous one left off and adds further opinions. In the previous mishnah we learned about a window of three days before the festival plus the day of the festival itself - a window of four days.
The opinion of Rabbi Yishmael:
"Rabbi Yishmael omer: sheloshah yamim lifneihen usheloshah yamim le'achareihen assur" - the prohibitions listed in the previous mishnah, doing business with an idolater and lending to him or borrowing from him, are not limited to four days as the first tanna holds, but extend to seven days: three days before the festival, the day of the festival itself, and three days afterward. The reason: the influence of the festival continues even after it, and the non-Jew attributes whatever happens to him in the days following the festival to the festival itself, and in the end he will come to praise his idolatry for it.
The opinion of the Sages:
"VaChachamim omrim: lifnei eideihen assur, le'achareihen mutar" - the Sages disagree and hold that the restrictions apply only before the festival and during it. After the festival we are not concerned that the non-Jew will retroactively attribute things to his idolatry, and the celebration does not continue beyond the day of the festival.
At first glance it sounds as though the Sages are simply repeating the opinion of the first tanna in the previous mishnah, but the Gemara explains that this is not so; rather, this is a third opinion. Mishnah 1 speaks of three days before the festival plus the day of the festival itself - four days in all; whereas according to the Sages in our mishnah it is only three days - two days before the festival and the day of the festival itself.
The practical halachah:
There are two levels to consider here. First, the Shulchan Aruch rules that these laws were stated regarding Eretz Yisrael alone, whereas outside of Eretz Yisrael the halachah is far more lenient, and the restriction applies only on the day of the festival itself. Several reasons are given for this:
Economic dependence: Jews outside of Eretz Yisrael were dependent on non-Jews for their livelihood. Someone doing business in a city where most of the residents are not Jewish will inevitably have customers from the non-Jewish population.
Darkei shalom: An open and sustained refusal to do business is liable to create bad feeling and hostility, and thereby endanger the Jewish population.
The level of religious commitment: There is an opinion that the non-Jews outside of Eretz Yisrael are not so religious and do not take their religion very seriously, unlike in Eretz Yisrael, which is a land of religious intensity, where even the idolaters are more serious about their religion.
In any case, whatever the reason may be, outside of Eretz Yisrael the prohibition applies only on the day of the festival itself.
The bottom line:
In practice, the Shulchan Aruch writes that nowadays people do not take idolatry seriously, and this is especially true in the Western world where most Jews live today. Even when it comes to their holiday, which by its very name is technically something of a pagan festival, they do not take the idolatry seriously and they do not praise it by name. It therefore appears that the practice today, which the Shulchan Aruch even endorses, is that these prohibitions no longer apply at all.