Taking someone's money without permission is also illegal - but that's not really the case here. When you agreed to pay them for the year, you gave them the permission to take it from you in monthly installments. If you want to make the argument that you pay for each month for the services rendered - that's not the case, otherwise you should pay a lot less for Tishrei and Nissan than you do for Cheshvan and Shvat.
Clearly it's not "All Rabbanim" - I imagine the Rabbanim advising the yeshivos to continue processing payment would disagree with your statement.
I can't speak for other schools, but I know from the contracts I've signed in both the Yeshivish World and the MO world, your tuition is an Annual fee, and the wording is something along the lines of:
"Tuition for grade X is Y per year. By signing, you accept responsibility to pay this amount. You can pay Y up front before the school year, or you can pay Z per month with post-dated checks or using our payment system".
So there is a shtar, where you accepted responsibility for the full amount + whatever tnaim are in the contract. I would have to think that when yeshivas draw those up, they consult both Rabbonim and a lawyer.
Again, I'm basing on my experience, but yours might be different.
Part of the X amount for full year is "this is our operation calendar that covers amount of days we are open and closed, with the allowance / exception that we may be closed for an extra few days if something like a major snowstorm type thing happens".
They count all the open days, assign daily cost / value = total for the year. Monthly installments is just splitting the bill.
Personally, my kids preschool (closed halfway through March) said:
A: We're keeping all tuition for March. We can provide tax deductible receipts for the associated weeks that school was closed since "goods not received".
B: We're not charging anything for April, until we know if / when we're reopening (if open for partial, will prorate those weeks).
C: Together with both of those, please whoever can, feel free to donate to us some / full / extra tuition to help support our teachers and staff during this trying time.