The song “Pomp & Circumstance” is in the public domain.
Is it permissible for students to play this music while being recorded and for the district to stream it live as well as distribute a link to the recording later?
Not only can the students play, record, and stream “Pomp & Circumstance,” but they can also create an original musical based on it, rap over it, score an original movie with it, and in short: do anything they want with it.
While anyone graduating in 2020 deserves this kind of red-carpet legal treatment, not only can the students do it, but everyone else can, too. That is the beauty of a work being in “the public domain.”
Thanks, and may all your virtual ceremonies be joyous.
 That said, any publisher that has created and distributed its own version of “Pomp and Circumstance” with a specific arrangement, illustrations, instructions, etc. may own the copyright to that particular text, and it shouldn’t be duplicated via hard copy or scanning. In a similar vein, any publisher that has issued a specific recording may own the rights to that specific recording, and that should not be streamed or used without permission, either. But the composition of “Pomp and Circumstance” is in the public domain, so generating a student-created version of it is fine, and if the district is the one recording it, they (and the performers) own the copyright (see Copyright Office Circular 56)!
 “In the public domain” means “no longer protected by copyright.” Edward Elgar, composer of “Pomp & Circumstance,” died in 1934, so even under the most rigorous scheme of ownership, the copyright to P&C has expired.