Pepper Jack cheese is not considered toxic to dogs but it should still be avoided for a number of reasons. A small piece is likely to be okay but anything more may cause gastric problems. Cheese in general is known for having a high fat content so dogs that eat pepper jack cheese on a regular basis may eventually suffer from long-term health issues like obesity and pancreatitis.
Dogs that have high intolerance to lactose will also suffer from eating cheese. Pepper jack cheese is known to have a lower amount of lactose than other cheese types but the lactose content might still be enough to cause problems in the dog’s stomach.
One last thing you also need to consider is the pepper that goes into this cheese. Some pepper jack cheese may use variety of peppers that are hot and fiery, such as jalapenos and habaneros. The ingestion of these peppers may cause further stress to the dog’s gastrointestinal tract.