First, a little historical background.
All of the hundreds of ancient images of menorahs ever found look roughly like the menorah used by the Government of Israel on its seal. The branches are curved. Here are three examples.
1. Hasmonean coin minted while the Temple stood by people – the Hasmonean dynasty – who also served as High Priests, who personally lit the menorah, and who knew what it looked like:
2. Magdala synagogue. 1st Century CE. Built while the Temple stood. Kohanim, priests, from the area would have served in the Temple and seen the menorah first hand:
3. Arch of Titus. Located in Rome and made as a commemoration of the sacking of Jerusalem and the Temple by artists who saw the parade of Jewish captives carrying the Temple vessels:
The only menorah that appears to differ from the curved/round branch variety is a menorah drawn by Maimonides late in the 12th Century CE. – 1100 years after the Temple's destruction. But this drawing, which was meant to explain aspects of the construction of the menorah, is really a schematic, not a literal representation. In fact, if you look closely you can see that the oil cup on the far right could not even hold oil, that the menorah would have burned unevenly, and that the penultimate oil cups on both right and left would probably not have been able to stay lit due to the angle of the cup. You'll also notice that the equivalent right branches' cups for the most part do not mach the left branches' cups in angle or in size:
Despite all this incontrovertible evidence, the late Chabad-Lubavitcher Rebbe Menachem Mendel Schneerson argued – without any evidence at all to support him – that the Rambam's schematic drawing was, in fact, a literal drawing of the Temple menorah. Chabad adopted the angular branched menorah as the "authentic" Temple menorah style and proliferated it across the world – again doing so without a shred of evidence to support it:
Now the Crown Heights Beis Din has taken this cultish insanity a giant step further by ruling that menorahs lit by Jews on Hanukkah must have angular branches – a claim that has no basis in history and no basis in halakha. In fact, despite the claim made by the Crown Heights Beit Din, Maimonides (the Rambam) never ruled that the Temple menorah must have angular branches, and he certainly never ruled that a Hanukkah menorah must – in fact, the opposite is clearly true. But this halakhic fact did not stop the Crown Heights Beis Din, as you can see here:
That's right. The menorah Jews light for Hanukkah should not, "to make a separation between the holy and the profane," look like the menorah with curved branches shown on the Arch of Titus, which is impure.
[Hat Tip: Maskil.]