Emblems used in Shrines and Temples
You might know each shrines and temples has own emblems as same as Samurai Family.
I visited Samukawa Shrine, in Fujisawa city, and asked some questions to Shinto priest in there. I would like to consider the relationship between those emblems, Mosque where Arabesque is used, and Family crest.
Emblems that are used in shrines and temples are also categorized as Kamon, family crest, too since those who administrate shrines and temples are kinship family of court noble. Specifically, Samukawa shrines uses symbols called Tomoe and Kikukamonsho, the Chrysanthemum Throne at many places. Tomoe is the one of the designs on the decoration on top of construction and door, and even on priest's clothes. Kikumonsho is used on Japanese lanterns. That symbol is also used on Japanese passport and something related to Emperor's family, which means it has very religious and strong meaning to Japan.
What I want to focus on is that they rarely use any Kanji characters like family crest of samurai. Moreover, they use weeds and flours for other decorations as same as mosque itself and design of arabesque in mosque. However, those botanical designs on shrines are not similar to ones on mosque. Specifically, as I introduced, flour designs in arabesque depict eternalness and ownership, but those on Japanese architecture such as shrines or castles show perishability.
Therefore, I consider those religious organizations implicitly tend to use those designs since they do not aim to express or emphasize personal thoughts.