So it looks like for most people the clothing isn't terribly important, but the etiquette is very important. Actions over appearance.
This is pretty much a discussion that can only be had with gendai arts like Aikido. The koryu arts are pretty clear about how much change is acceptable (not much. You either adapt yourself to the system or go do something else).
I will note that as far as I'm concerned, modern IJF Judo is almost a completely different animal from the Kodokan Judo from which it was born. They still use the cloths and the formal etiquette and the Japanese terms, but the spirit of practice has been transformed. The complete focus on competition and making everything spectator and TV friendly has created a completely different beast with a totally different soul.
I don't think it is easy to say clothes are or are not important. My answer is "it depends". Spending my time in BJJ these days I have seen many variations of teaching styles. I have been to gyms that pump up there students with Angry White Boy music and others that play very relaxing euro beat music. Most don't play music at all. Some will bow in and out, some will not. Some only allow white gis, others you can wear a pink one with patches! However, the quality of the jiu jitsu tends to be decent regardless...so you might surmise that "it doesn't matter".
However, I'd argue that it does matter in some respect. I might play relaxing euro beat music and dim the lights and try and create an ambiance that relaxes the students and gets them to flow. Other times I might cut off the AC, play loud music and increase the stress.
It all depends on the students and teaching style of the teacher and how he uses the environment to connect and reach his students.
Customs and courtesies must be important as we have them in the military. They matter for what they are, but they are NOT everything. They help encourage "good order and discipline" for the masses, establish an identity, and create brotherhood and affinity. Outside of that, I don't think it matters much.
So, is it still aikido without all this. I think so. I think you most certainly can call your art Aikido if you are following the tenants of your methodology and are working successfully to achieve your end states.
Alas, "what is aikido?" "how do we know it when we see it". of course, we spend a great deal of time defining what this means as it is an elusive art that seems to escape the ability to objectify measurements of effectiveness!
I think sometimes putting on the hakama is a good thing. but it can also be a hinderance, just as a black belt can be a hinderance if we start believing the myth of our belt!