Mormons

Mormons believe they belong to the Jewish lost tribe Ephraim, and that's why Judaism is so important for them. No wonder they use the Star of David:
The Salt Lake Assembly Hall is Victorian gothic building and a Star of David within a circle is placed high above each entrance. (Photo courtesy of Wikipedia).
Some of the Mormons believe that the Star of David got its shape from the Urim and Thummim that the Jewish High Priest carried on his chest.
Vincent Chapman published on 28 January 2005 a flag for the Mormon Church which contains a big Star of David in the center surrounded by twelve stars that stand for the twelve tribes and the twelve apostles. The former Mormon flag which was made in the 1800's by Emma Smith had a large 5 point star in the middle.
Utah Republican Mormon Senator, Orrin Hatch, is a Zionist and on his front door there's a Star of David.
Cecil McGavin in his book Mormonism and Masonry (2004) mentions that Joseph Smith, the founder of the Mormon Church, "was not a Jew yet he was pleased to display above the door in his historic Mansion House in Nauvoo, Illinois, a small gilt-covered six pointed star".

Little-Known Chapter

Mildenstein medal, with a Swastika on one side and a Star of David on the other 
Photograph courtesy of Arnon Goldfinger (c) 2014

Mark Weber, Director of the Institute for Historical Review, published an article about Zionism and the Third Reich and in it told the story of SS officer Leopold von Mildenstein and Zionist Federation official Kurt Tuchler who traveled to Palestine together and stayed there for six months in order to assess Zionist development. In 1934 von Mildenstein published twelve illustrated articles in Der Angriff. Der Angriff issued a special medal, with a Swastika on one side and a Star of David on the other, to commemorate the joint SS-Zionist visit.

In the introduction to this article Weber says that this is one of the stories belonging to the little-known wide-ranging collaboration between Zionism and Nazi authorities; I reckon it is a repressed chapter, certainly from the Zionist point of view.

P.S.
 See Arnon Goldfinger's 2012 documentary, The Flat, on:
https://www.youtube.com/watch?v=Z94u_5qLxXU#t=30

See Also:
en.wikipedia.org/wiki/The_Flat_(2011_film)