I'm on Anna's side with this. A leave-taking ceremony, an awards ceremony--fine. Caps and gowns? Premature and, to me, pretentious. "Diplomas"? Seriously? They haven't earned anything. If you have to give a piece of paper, call it a certificate. This is the pedantic part of me coming to the fore--you earn a diploma when you are graduated from high school. It cheapens the worth of that diploma to call an eight-grade leaving certificate a "diploma."
If I were Anna, this is what I'd do.
I'd bring the matter up to the school. It could very well be that there are other parents who feel the ceremony has gotten out of hand and who would welcome cutting back on the excess trappings. Or parents who can't really afford to buy or rent the cap and gown, but feel forced into doing so, so that their child will not stand out. I don't see any real reason why she can't make her thoughts on the matter known, in a calm and polite way.
It is not SS behavior to state that you don't like this one particular aspect of the school. If a parent can have input on the dress code, or the detention policy or any other part of school life, they can have their say about the leave-taking ceremony as well.
Then I'd talk about it with the child, making my views known and the reasons behind them.
Then I'd let the kid make up his/her mind about attending the ceremony. Depending on how strongly I felt about it, if the child decided to participate in the ceremony, I might make them pay for the cap and gown, through their allowance and paying for odd jobs they would do around the house. Or I might give them the money for the cap and gown and tell them they can either spend it on the cap and gown to attend the ceremony OR they can not attend the ceremony and spend it as they choose. Or I might offer a choice between the attending the ceremony or attending SuperFunPark or other interesting/fun/educational place, like an natural history museum or National Park.
If they choose to attend and they wanted me there, I'd go.
I would also make it clear to the child that, no matter what they decided, there would be the standard at-home family celebration for a member of the family that has achieved a milestone--the family party, with cake and silly jokes and probably a small present to mark the occasion.
For something like this, there will probably be practices for a few weeks ahead of time. It can be very painful to kids at this age to be singled out and separated from the group. It's a delicate balance between the parents' standards and not making school life too difficult for the kids.
I know, my parents had very strict, rigorous beliefs about a lot of things, and I spent most of middle and high school as the different kid who dressed funny, couldn't go to parties or dances and in many other ways stuck out like a sore thumb. So while I dislike many of the aspects of the ceremony described in the OP, I would be very careful about forbidding my child to take part in it.