Mike Dorf with an interesting post about whether, during a visit to a Buddhist monastery, he should move grains of incense as an offering. He explains why he (a cultural Jew) elected not to it, linking it to the way in which Japanese people move freely between Eastern religions, whereas Abrahamic religions are more exclusive.
I want to think of this as Westerners viewing non-Abrahamic religions (not only Eastern but also Native American or African) less as religions and more as generic rituals or practices. People do lots of things for general good luck or, pejoratively, superstition. At Bryn Mawr, students leave offerings at a statute of Athena; at Northwestern, we would rub the nose on the bust of Joseph Medill (the 19th c newspaper editor after whom the J-school is named) before taking exams in that building. I would never think of this as idolatry, because none are directed at what we understand to be a deity or part of a (current) religion.
Or consider reality competition shows filming outside the US (Survivor, Amazing Race). They often have contestants make offerings or otherwise participate in rituals (watered-down, to be sure) for local non-Abrahamic religions. But I do not recall them, say, having contestants light votive candles in Italy or join in the Fajr in Kuwait. The producers would see that as offensive to the contestants (most of whom are either non-religious or belong to Abrahamic faiths) who do not adhere to the religion and to the adherents of the religion. This reflects the lack of fluidity Dorf describes. But it also reflects that we see Catholicism or Islam as religions in a way that we do not see Buddhism. Contestant offerings in Buddhist monastery or on a reservation are seen as more akin to leaving a penny for Athena in advance of an Orgo exam.