Is there, aside from Secular Buddhism, a sect or tradition of Buddhism that does not include rituals and chanting as a part of it's liturgy?
Yes. The "original tradition" i.e. of the time of the Buddha himself, did not have a lot of the rituals and customs that are practised today.
There was some recitation of the Dhamma and Vinaya, but it did not amount to liturgical chanting in the Buddha's time. Certainly, monks did not chant for blessing, in the Buddha's time. Recitation was just a form of recollection, as it was initially an oral tradition. Recitation of the Dhamma and Vinaya did not have mystical effects.
There were no statues or idols or images in the Buddha's time, and certainly no rituals were performed to those idols or images. There were stupas, as we could find in DN 16, but those were just memorials for inspiration and not for worship. In fact, the tradition of making Buddha images originated centuries after the Buddha, influenced by ancient Greek art.
There were no Buddhist temples in those times. Only monasteries and some stupas.
The Buddha strongly criticized astrology, palmistry, divination and such practices in DN 2.
Prayer beads or rosaries, mandalas, incense etc. all came much later and was not part of the original tradition.
Chanting isn't necessarily ritualistic but it can be. Probably no such traditions.
The way people worship nowadays with statues and rituals seems to have gained popularity some 500 after Buddha's death.
There is a version of a pali vinaya that has a story of Buddha not allowing statues of him be built but making an allowance for the statue of a Bodhisatta. Either way the Earliest Buddhist imagery is exclusively footprints and symbolism.
I guess some people don't care much for the rituals but it's deeply established in populations and is more or less present in most if not all communities.
The common cultural traditions and buildings are for the utter most part no older than 300 years.