There is a religious group of Esperantists in Japan that consider Zamenhoff to be one of many gods. The religion is called Oomoto.

Has anyone had contact with this group and would you care to share your experience?

Alkanadi:There is a religious group of Esperantists in Japan that consider Zamenhoff to be one of many gods. The religion is called Oomoto.

Has anyone had contact with this group and would you care to share your experience?

No, I have not. Though I do know something of what you're talking about, I provided some of the content for that article.

This isn't the only religion to have a significant interaction with the Esperanto movement.

• There was/is a group called the Catholic Esperanto League....
  
• Bahá'í have a relationship with the Esperanto movement that I don't fully understand. Lidja Zamenhof (LL Zamenhof's daughter) converted to the religion (from Judaism) and was an early proponent of the faith.
  
• I don't understand the current connection between the Bahá'í movement and Esperanto. I don't think Esperanto is used liturgically or anything like that. (I wonder if someone could comment on that point.)
  
• There was also Zamenhof's attempt at Hillism and his own brand of theistic-humanism.

There is probably more, but that's all I can think of at the moment.

eojeff:There is probably more, but that's all I can think of at the moment.

Also, the Quakers. I recently heard that in Brazil most Esperantists are involved in some spiritual movement. As for non-religious, there seems to be a lot of Esperantists that are communists.

Maybe, religion/ideologies are good tools for spreading the language.

eojeff: There was/is a group called the Catholic Esperanto League....

I don't think Esperanto is used liturgically or anything like that. (I wonder if someone could comment on that point.)

IKUE, la Internacia Katolika Unuigxo Esperantista, is alive and well so far as I know. IKUE Still producing 'Espero Katolika' since 1903. EK More information on Vikipedio here Vikipedio

If you really love monotone broadcasting you'll love these from Radio Vatikana! Arkivo

As regards liturgy, there is a Vatican approved translation of the Mass into Esperanto, which was promulgated some time around 1993. It comes in two volumes, the Missal and the Lectionary of readings. It is for Sundays and major feastdays only, if memory serves me well. I don't think priests have the freedom to just pick up the Missal and say an Esperanto Mass at will. My understanding of the situation twenty years ago was that an Esperanto Mass may be celebrated if the common language of the congregants is Esperanto. e.g. an Esperanto Mass for the local Esperanto club in Rome, where they all speak Italian, would not be permitted unless there were some kind of gathering of Esperantists from other native language communities. I do know a Scottish priest who has said Mass in Esperanto in Scotland in those circumstances at a Skota Kongreso.

La 8an de novembro 1990 la vatikana Kongregacio pri la Dia kulto kaj la disciplino de la sakramentoj aprobis la mestekstojn en Esperanto. Tiamaniere Esperanto definitive fariĝis liturgia lingvo. Ekde somero 1995 la "Meslibro kaj Legaĵaro por dimanĉoj kaj festoj" estas havebla en formo de du lukse binditaj volumoj.

[from the Vikipedio page linked above]

My memory is indeed getting faulty...