BJJ is not a budo. It's just a series of techniques. It has no spiritual content. I am of the opinion that in Japanese arts everything has meaning and tradition. This includes the clothing and the protocol in the dojo. If you remove those things you might just as well go outside and roll in the dirt. Just my opinion.
First of all, both aikido and BJJ are as "spiritual" as the practitioner chooses to make them. It is entirely possible to practice BJJ spiritually, and entirely possible to practice aikido nonspiritually.
In terms of the specific traditional trappings of aikido, I have two stories that I think are very relevant to this thread:
Ikeda Shihan visits my old club every year for a seminar. One year, his luggage did not arrive with him, and he therefore had no uniform for the Friday night class. Many students and instructors were falling over themselves to offer him their gis and hakamas, but he waved them all off politely and led the class in jeans and a tee shirt. I can assure you all that his aikido was just as real that night as any other night.
Aikidoists from all over the Milwaukee area get together in the summer to train with weapons out in the park. There are no gis or hakamas, there is no sitting in seiza, and there is no kamiza to bow to, and our aikido is none the worse for it.
The more I train, the more I come to think of the uniform, the bowing, the etiquette, the kamiza, etc. as non-essential. I am happy to have them, and I am not suggesting we get rid of them, but I think it's dangerous to start imbuing trappings with some kind of pseudo-religious importance. The real essence of aikido, I think, is not in what we say or wear.