I'm now kind of upset at myself that I have thrown out perfectly good Cheddar in the past due to white spots.
Also, if you get bright white(!) spots on cheese like Brie (which is made with white fungus), it's usually just the cheese "reactivating". You - theoretically - don't even need to cut off anything.
I’ve eaten brie weeks after sell by date. It just turns into a firmer cheese by then no striking difference in taste really.