Is Rokuyō a religion?

Rokuyō has a linguistic connection with Buddhism. Does that mean Rokuyō is a religious tool?

Well, you'll have noticed that Rokuyō is highly balanced, with symmetrically reversed meanings across its six days:

Rokuyō is also quite balanced with an equal amount of  good fortune  and  misfortune,  as shown in this Fortune Indicator:

This emphasis on balance echoes Onmyō (yin–yang) thought, a cosmological system historically associated with Daoism and Onmyōdō in Japan. While Rokuyō contains Buddhist terminology and exists within Japan’s broader syncretic culture (where Buddhism, Shinto and Daoist ideas historically overlapped), this doesn't make Rokuyō a religion in the generally accepted sense of the word.

The calendar used for Rokuyō follows a lunisolar structure, noting new moons in a way broadly comparable to the Old Farmer’s Almanac (sometimes jokingly called a U.S. gardener’s “bible”). That almanac combines weather forecasts, astronomy, agriculture and folklore. It's been published every year since 1792, making it one of the oldest continuously published periodicals in the world. But it's not part of a religion.

In coastal regions of Vietnam and the Philippines, traditional lunar-based systems are still used by secular fishing communities to estimate tides and favourable fishing nights. These practices are practical and cultural, not religious.

Lunar and lunisolar calendars are indeed used by religion; for example, the Islamic calendar, the Hebrew calendar, the Hindu calendars, the Buddhist calendar and the Tibetan calendar. These calendars determine religious observances such as Ramadan and Passover, and they are also used for calendrical festivals such as Lunar New Year in East Asian traditions..

And of course Christianity likewise uses the lunisolar calculations to determine the date of Easter and other movable feasts. But as with most other major religions, fortune-telling and superstition in general is taboo.

Religion has no need for Rokuyō.