Answer:
No, their music is not very similar.
These 45 living composers are current members (or "Academicians") of the American Academy of Arts and Letters. They form an elite group of shakers and movers in American concert music. Once appointed, they hold this distinguished post for life.
The only way to become a member of the club is to be nominated and elected into it by other Academicians. It's a self-sustaining system where since 1898, new members continually replace the ones who pass away.
The Academy's composer-members who have died in recent years include Miriam Gideon, Norman Dello Joio, Henry Brant, Donald Martino, George Perle, Francis Thorne, and Andrew Imbrie. The average age of current Academicians is probably around 78. I've heard that some of the members who attend the meetings need to be accompanied by their private nurse.
Membership for all disciplines is limited by the Academy to exactly 250 members. Besides composers, membership includes architects, artists, and writers. Once elected, there are no dues. Annual dinner meetings are held at their classy Beaux Arts campus on Broadway at West 155th Street in upper Manhattan. In addition to the prestige and honor of becoming a member, professional networking opportunities are abound.
The Academy confers annual cash awards ranging from $5000 to $75,000 to external recipients who are are selected by committees drawn from the Academy’s roster. Members of the society recommend and decide how to allocate those generous funds, and it is typically awarded to their students.
I don't know if members of the Academy consider themselves Illuminati, but there certainly is an air of secrecy around the society's behind-closed-door activities. The organization is a mega-center of influence and power, even though the general public is barely aware of its' existence. It's a little like the mysterious Trilateral Commission or the secret society at Yale known as Skull and Bones. Membership is by invitation only, but once your in, you're "in."
I've often wondered what goes on behind those closed doors. What deals are made? How do those strong personalities get along with one another? How do they decide the future of American art, music, architecture, and literature with their vote of approval or disapproval? It's ripe with potential source material for a Dan Brown style novel. The backdrop of the Academy could provide a basis for a complex plot involving conspiracy theories, politics, and intrigue. The action-movie version of this bizarre scenario runs rampant in my imagination.
Links:
http://www.artsandletters.org/about_history.php
http://en.wikipedia.org/wiki/The_American_Academy_of_Arts_and_Letters