That's the hard part, it is not about respect in this case, it is about faith. These are very different things. The rules of entry for Aikido once make it nearly impossible for Westerns to practice. Eventually O'Sensei saw this was wrong since Aikido is for all mankind, not just Japanese. How are we keeping to his ideas if we knowingly mandate requirements that force students to leave? Is the spirit of Aikido lost if one doesn't bow?
If one cannot make the simple adjustment to Japanese culture of bowing in a secular context of etiquette, how can one expect to really get the "spirit of Aikido"? A spirit born of Confucian, Buddhist, and Shinto beliefs?