The National Association of Secondary School Principals has a
"National Advisory List of Approved Student Contests and Activities" and FRC is on the list. (The Program Guidelines are
here.) I don't know if it will help convince your school's principal and administration, but you should make sure that they know about the list. Making sure that everyone else involved (parents, school district, 4-H organization, etc.) is also aware of it is important too. The fact that the trip was approved by the school district before it was taken is important to point out too.
We are no longer sponsored by our school district and we have students from several different schools (and school districts). We have successfully gotten absences excused for competition days, thanks to our logistics mentor working closely with the various administrations.