Hi Erik,
“Rent” is the money that you pay the owner/landlord of the place you’re living (it can be a house, apartment, etc).
“Due” is an adjective here meaning the expected time of arrival. Also with rent, it’s the last day (or deadline) that you have to pay.
Ex: If rent is due on January 5, you must pay the owner (landlord) on January 5 or before, but not after. (Or there could be consequences)
Therefore, “Rent shouldn’t be due” means the rent $$ should NOT be due (on a specific date)
For instance: Imagine the owner of an apartment knows the people living in his apartment (also called tenants) can’t work due to Coronavirus. Someone may comment “Rent shouldn’t be due on April 5. The landlord should give them extra time.”
And depending on the context, it’s another way for people to simply say that the rent isn’t due now, but that it’s due in the future.