Over the years, I have been exposed to dojos that opened every class with the Shinto ritual of three claps, bow, three claps.
Other dojos read from the writings of the Founder or Koichi Tohei, Sensei, or someone else. This latter reminds me of the lay reading in most churches.
My two lead instructors did not do either of these, in one case, Kobayashi Sensei, when asked about the clapping, responded that he was Buddhist, not Shinto. Of course he also gave the same response when asked if there was going to be class on Easter Sunday.
In my dojo, I have scheduled Misogi on every Saturday morning for 1 hour. Most times we just sit and breathe. Sometimes we practice Aiki Ryoho (Kiatsu). Other times we breathe with a particular focused meditation.
I have found that as long as I do not make a big fuss about the depth of oriental philosophy behind Misogi, many people participate regularly. If the oriental philosophy is over emphasized, some people automatically exclude themselves because of their belief system.
My main point of annoyance with some of the practices passed off as being "spiritual Aikido" is the overly mystical manner by they are "explained".
Such explanations tend to emphasize that the person giving the explanation is somehow on a different spiritual plane that the rest of us poor unenlightened ones. As if incomprehensibility is the same as depth of understanding. Consequently, the student has little idea of how to make the practice relate to them.
Since I teach both Chinese and Japanese Culture and philosophy, I have developed a profound respect for the depth behind some of the beliefs. I also am aware that some practices were developed in reaction to the standard beliefs of the day and were intended to set that particular group apart from the rest of the world. Cf. The Catalpa Bow for an examination of shamanism is Japan.
For me it has come down to the following test:
How well do my arts reflect my spiritual understanding, and, how well is my spiritual understanding derived and based in my arts?