I did a little digging around and reading about your school. Correct me if I am wrong but it seems that your school is 'no slouch' and is aspiring to greatness. ( there are plenty of schools satisfied with the status quo ).
If I interpret their website correctly your fundamental problem isn't that they don't support the team. Your team's fundamental problem is the administration doesn't "get it" !!
They probably do not have an understanding of the FIRST mission, why it is important to our future and how the school and students are a part of the solution. They almost certainly view the team as bunch of nerdy hobbyists and do not connect it to national priorities.
They have not gotten the message : from their website
It is your team's responsibility to educate them. I would suggest enlisting a cool headed mentor that is good at communications and ask for their support in conveying the message.
The school measures their success by the academic scores of their student and the college placements they make.
The national stakeholders of FIRST, the over 3,500 companies and Universities that partner with FIRST have another opinion on the subject. And that opinion is that if you are going to make bold statements like on their web page ( listed above ) and it doesn't have FIRST and/or a similar high profile STEM activities listed, then they are just blowing a lot of smoke.
It they were a 'normal' school I could see them they acting the way they do. But if they are going to "talk the talk" then they are going to have to "walk the walk".
Re-think the issue and figure out how to explain it to them.