"I wish there was just a toggle that would turn this off."

Yes, you can turn off the printing of it.

Yes, you control if it is Past Due or not factually, by how you handle the Due date, the terms, and this makes your Aging report correct. Are you running your AR aging Summary report, to manage this?

Don't ignore something as meaningful as Due dates. Manage them.

"This is a huge pain because I have a lot of customers"

Edit Customers to assign their Default terms; it is easiest to use Lists menu > Add/Edit Multiple.

Fix Open Invoices, to get on track. QB will do the rest, from now on.

Done.