Indigenous religions (19)
http://www.worldheritagesite.org/categories/category16.html

Dazu
Fujisan
Great Burkhan Khaldun
Huangshan
Itsukushima
Jongmyo
Kii
Lushan
Qingcheng and Dujiangyan
Taishan
Wuyi
Niko
Osun-Osogbo
Temple of Heaven Beijing
Confucius
Buganda (Kasubi)
Tongariro
Tsodilo
Wudang

Some other sites may qualify:
SGang Gwaay, Ambohimanga, Mijikenda, Konso, Bassari, Bandiagara, Roi Mata, Matobo, Sukur, Uluru

In this category, better to group the sites first.

For Taoism connection, Huangshan, Taishan, Wudang, Temple of Heaven, Qingcheng, Lushan, Dazu, Wuyi; Taishan is maybe the most important mountain in this group for its cultural importance. BUT for achitecture Temple of Heaven is really stunning and represent imperial ritual ceremony. Wudang is a replica of Beijing Imperial Palace and other sacred mountains don't have role like Taishan.

So For Taoism : Taishan and Temple of Heaven

Confucius : Jongmyo and Confucius at Qufu. The site at Qufu is the most important for Confucius and architecture for shrine and mansion are one of the best in East Asia.

So for Confucius: Qufu

Shinto: Fuji, NiÄ·ko, Itsukushima, Kii. While Fuji is very iconic, its Shinto element is not stand out. Nikko is amazing in architecture, but in my opinion, Itsukushima is really stunning for its design of floating in the sea with big torii gate, a good representative for Japanese Shinto architecture.

Shinto: Itsukushima

No idea on Africa and Pacific

I would additionally pick:
SGang Gwaay - a unique site in reflecting indigenous religion in the America
For the Pacific we would have Tongariro, Roi Mata and Uluru. Roi Mata represents Pacific tabu systems and small island societies. From Tongariro and Uluru I would pick Uluru as Australian because of its impressive landscape and significance for various aboriginal cultures.
For Africa I would probably vote for Ambohimanga over Buganda to represent the cult of royalties as it encompasses more elements. I would choose one grove (Osun-Osogbo or Mijikenda). I would also choose a site involving rock art (Matobo or Tsodilo). I don't enough to choose between Konso, Sukur, Bassari and Bandiagara.

My selection:

Qufu for Confucius
Temple of Heaven - Taoism, iconic
Itsukushima - iconic, serene natural surroundings as a continuation to the religious atmosphere and traditions, Shinto
Uluru - iconic, great example of symbiosis of nature and religion in Oceania

My selection:

Huangshan
Itsukushima
Taishan
Temple of Heaven Beijing
Confucius
Wudang

Full Support
Temple of Heaven- Obvious significance and wooden architecture design is exceptional.
Itsukushima - Shinto relgious site and living tradition

Confucianism is rather difficult. Should we select and recognize Qufu (perhaps better recognized in Residences), which is undoubtably important, but mostly today a tourist mansion of the most prominent non-royal family in China? Or should we consider where Confucianism is the strongest manifestation both in the sites use and how impactful its been on its people (including today)? If its the latter, than one of Korea's Confucian sites is arguably more appropriate then China.

Jongmyo - MAYBE Ceremonial center and longstanding traditions that span then entire Joseon Dynasty (ancestry worship, Confucian ceremonies). Includes inscriptions on the Intangible Heritage list. Sometimes called the "Parthenon of Asia" though I cannot give my full support to this assertion or its candidacy of Top 400. Check the review section for both Els and my own review if you haven't visited. Important yes, exciting or iconic not as much.

Hahoe and Yangdong (not listed) - MAYBE 3 Confucian Academies, includes inscriptions on the Memory of the World Register.

Royal Joseon Tombs (not listed, also tomb category?) - MAYBE Blend of Feng Shui and Confucian traditions, exceptional because it preserves the burial tradition and tombs of an entire dynasty spanning seven centuries (14th to 20th).

Criterion (iii): Within the context of Confucian cultures, the integrated approach of the Royal Tombs of Joseon to nature and the universe has resulted in a distinctive and significant funeral tradition. Through the application of pungsu principles and the retention of the natural landscape, a memorable type of sacred place has been created for the practice of ancestral rituals.

Criterion (iv): The Royal Tombs of Joseon are an outstanding example of a type of architectural ensemble and landscape that illustrates a significant stage in the development of burial mounds within the context of Korean and East Asian tombs. The royal tombs, in their response to settings and in their unique (and regularized) configuration of buildings, structures and related elements, manifest and reinforce the centuries old tradition and living practice of ancestral worship through a prescribed series of rituals.

Criterion (vi): The Royal Tombs of Joseon are directly associated with a living tradition of ancestral worship through the performance of prescribed rites. During the Joseon period, state ancestral rites were held regularly, and except for periods of political turmoil in the last century, they have been conducted on an annual basis by the Royal Family Organization and the worshipping society for each royal tomb.

Don't forget to pick sites from outside Asia. There are some candidates for Africa, Oceania and one from North America.

My selection

Temple of Heaven
Itsukushima
Qufu for Confucius

While I've long been interested in this WHS, the criteria does not mention religion and the description of the sites is primarily focused on art. I am certainly not against including here, but I did not see much justification regarding religious traditions. Or did I miss something?

You are right I think. Totem poles are not religious objects.
I think it's best to leave the site at Archeological, Pre-Columbian

It seems that we're messing this one up a bit.
Let's go back to the start & the grouping proposed by Durian.

Taoism: Huangshan, Taishan, Wudang, Temple of Heaven, Qingcheng, Lushan, Dazu, Wuyi
Confucianism : Jongmyo and Confucius at Qufu.
Shinto: Fuji, NiÄ·ko, Itsukushima, Kii.
Maori: Tongariro
Shamanic: Great Burkhan Khaldun
African: Osun-Osogbo (Yoruba), Kasubi Tombs (Buganda), Tsodilo (San) (maybe better move to Rock Art)

I would leave discussion on any additional sites elsewhere, although they may have similarities. Rock art etc will have their own discussions later.

Temple of Heaven - Ceremonial location for dynastic legitimacy, Ming Dynasty architectural masterpiece
Itsukushima - Quintessential Shinto site
Qufu - Continuous reverence for Confucius and his decedents for over two millennia

Taoism: (included both aspects of taoism- Sacred mountain (Taishan, Wudang) and Daoist Temple (Temple of Heaven)
Confucianism : Confucius at Qufu
Shinto: Itsukushima

African can be covered in other categories.

My selection:

Taoism:
- Wudang - Y -(seems more impressive in terms of architecture than Taishan)
- Temple of Heaven - Y
- Dazu - Y - (for its carvings, already selected it also under Buddhism)

Confucianism :
- Jongmyo - N - might be unique, but it's an underwhelming site
- Confucius at Qufu - Y

Shinto:
- Itsukushima - Y
- Fuji - Maybe - iconic for Japan itself
- Nikko - Y - exceptional architecture

Maori:
- Tongariro - N - natural aspects seem more relevant

Shamanic:
- Great Burkhan Khaldun - N - too intangible for me

African:
- Osun-Osogbo (Yoruba) - Y - as per discussion in other thread
- Kasubi Tombs (Buganda) - don't really see the religious connection here; fits more with other mausolea
- Tsodilo (San) "maybe better move to Rock Art" - agree

This one is still missing a summary.