Even if you think budo is inherently religious/spiritual (that's an argument for another thread, I think) it's important to distinguish what is and is not budo. White uniforms, colored belts, bowing, seiza, the kamiza, Japanese phrases, even the dojo itself: to me, these things are not budo. They are the trappings that usually go along with budo, but I think budo would still be budo without them.
You misquoted me quoting you! I distinctly said "pseudo-religious."
Budo is a process meant to change and strengthen a practitioner along the lines of character, spirit, mental endurance, etc. It has to be a process that you submit to. You don't get to choose what it is. That would be like a military boot camp where recruits were allowed to choose how many hours of sleep they would like each day and what activities they chose to sign up for.
Of course modern military training is not pseudo-religious, but of course it is not based on principals laid out in Chinese classics either.