It is easy to see if mold is forming on block cheese. I have, many times over the years, simply excised moldy portions from blocks of cheese, rinsed the remainder with cold water and if it looked and smelled okay, tried a nibble. If I was satisfied that it still tasted good, I've gone right ahead and eaten it, with no ill effects.
Shredded cheese, on the other hand, can be difficult to evaluate. Usually, once shredded cheese starts to go bad, the whole bag picks up the smell and off flavor, rendering it garbage.
Of course, I am NOT recommending that anyone (including you) eat foods beyond their expiration dates and I would NOT risk anyone else' health with such gambles. I'm just sharing what seemingly silly, reckless behavior I've managed to get away with, unharmed. Your mileage may vary. Beware.