It's no secret that I observe one day of yom tov, following the Torah, the longtime practice of the land of Israel and the Reform movement, and the minhag of my ancestors for generations (being one of those fifth-generation Reform Jews who are pronounced nonexistent when it suits the rhetoric).
This post addresses a rarely-explored consequence.
Leviticus 23:40 commands only that the four species be taken on the first day, and says nothing about what should be done the other days of the holiday. Therefore, the Mishnah (Sukkah 3:12) says that outside of the Temple, the lulav (synecdoche for all four species) was taken only on the first day, and it was taken all 7 days in the Temple. (Sifra Emor 16:9 (I think? I don't know the proper citation format) derives this from the end of the same verse, where it says "you shall rejoice before God 7 days", suggesting that lulav should be taken 7 days when you're "before God", i.e. in the Temple. Thanks, EAR, for the Bar-Ilan login.)
According to the same mishnah, when the Temple was destroyed, Rabban Yochanan ben Zakkai decreed that the lulav should be taken all 7 days everywhere, in remembrance of the Temple. For those keeping track, lulav on the first day is still a Torah commandment, while lulav on the other 6 days (outside the Temple) is a rabbinic decree.
Later on, the Mishnah (Sukkah 4:1) says that the lulav is "6 and 7". That is, as elucidated in Sukkah 4:2, if the 1st day of Sukkot falls on Shabbat, the lulav is taken all 7 days, and if it falls on any other day of the week, the lulav is taken 6 days (every day except Shabbat).
Why? Rabbah explains in the Gemara (Sukkah 42b) that this is a decree to prevent people from carrying a lulav in the public domain on Shabbat, the same decree that applies to shofar and megillah. I don't quite see the point of this -- the Mishnah (Sukkah 3:13 and 4:3) already discusses solutions for benching lulav on Shabbat (in this case, when yom tov falls on Shabbat) without carrying on Shabbat, viz. everyone brought their lulavs to the synagogue/Temple before Shabbat, and when that got too ugly, they started benching lulav at home instead. I don't see why that couldn't work just as well for Shabbat Chol Hamo'ed. But even if I don't agree with Rabbah's reasons, I don't have a problem with this decree -- chaza"l gives and chaza"l takes away. The rabbis are the ones who established the practice of lulav on days 2-7 of Sukkot in the first place, so they get to impose constraints on it. But they don't impose any constraints on lulav on day 1 (at least the Mishnah and the earlier amoraim like Rabbah don't), because it's a Torah commandment that they can't overrule.
So, you ask (as does the Gemara, on Sukkah 43a), how do we get from there to the present-day practice that lulav is not done on Shabbat even when it's the 1st day of Sukkot? The Gemara answers that "we" (here in Bavel) don't know the correct date of the new moon in time for the holiday. So for the same reason that they observe 2 days of yom tov (because they don't know which one is the real 15th of Tishrei), the Torah commandment to take the lulav on the 1st day of Sukkot can't override Shabbat if this epistemological uncertainty means that they're not sure it's really the 1st day of Sukkot, so they might be breaking (an electrified fence around) Shabbat for nothing.
But wait a second, you ask (as does the Gemara), what about in Israel, where they observe 1 day of yom tov, since they're certain about which day is the real 15 Tishrei? Shouldn't they bench lulav on Shabbat when it's the 1st day of Sukkot, since it's definitely the 1st day of Sukkot, so the Torah commandment should win? The Gemara responds "In hachi nami." ("Yeah, you're right.") Oops.
To this day, in Israel, the most common practice is not to bench lulav on Shabbat, even when it's the 1st day of Sukkot. The Gemara provides evidence that this has been done for at least 1500 years, but was known to be erroneous 1500 years ago.
In I Samuel 8, the people ask Samuel to give them a king, and he gives them a list of reasons why this would be a bad thing, and they say that they want a king anyway. During the English Revolution, this chapter was used as a prooftext both by supporters and opponents of monarchy. There are two different possible responses to "They knew this was wrong, and did it anyway": 1) "See, they knew it was wrong!" 2) "See, they did it anyway!"
In this case (lulav for 1-day-yom-tov observers when the 1st day of Sukkot falls on Shabbat), I'm going with approach #1 and holding by the Talmud when it calls the practices of its own time mistaken, though there are also cases when I go with approach #2 (see: kitniyot). Therefore, I will bench lulav this Shabbat, as will the minyan that I am visiting (I presume for similar reasons).
In fairness to the other side, I'll present some later views. The Rambam (Hilchot Lulav 7:17) codifies the practice that the Gemara calls erroneous, but (unlike the Tur / Beit Yosef / Shulchan Aruch) gives a reason: so that everyone is equal, and the Israelis (1-day observers) and the Diaspora residents (2-day observers) aren't keeping two separate practices.
To that I respond, his desire for unity is all well and good, but it's way too late for that -- if the Diaspora is already keeping A WHOLE EXTRA DAY OF YOM TOV, then what's a lulav here and there? Also, if we're going to have everyone do the same thing, wouldn't it make more sense to have everyone bench lulav (and fulfill the Torah commandment) than to have everyone not bench lulav (and fulfill the rabbinic decree)?
In Hilchot Lulav 7:18, he says that this practice of not benching lulav on Shabbat, even on the 1st day, in both 1-day and 2-day communities, stands in the present time when we determine the calendar by calculation rather than by eyewitness testimony. But he provides no further explanation.
Chag sameach! May your holiday be nothing but happy.
UPDATE: See the comments. On the following daf (Sukkah 43b), the Gemara indeed says that Eretz Yisrael should follow the Diaspora and not shake the lulav on Shabbat. Does that invalidate this whole post? Not necessarily. See the discussion in the comments for more.