It depends on your dog. Some dogs are lactose intolerant, but loads of trainers suggest cheeses as high value training treats: The folks at fearfuldogs.com suggest a few cheese options. A local trainer who we hired -- Brooklyn Pup -- gave him bits of cheese as rewards. Whole dog journal suggests cottage and ricotta cheese in their recipes (they caution against high fat cheeses but suggest adding fats further down in the recipe so ...).
I had a dog as a kid who we definitely had to keep away from any cheeses. If he got his hands on basically anything, he'd eat it, cheese included, and his lactose intolerance ranged from flatulence (really bad flatulence) with small amounts (a stolen sandwich) to outright diarrhea with larger amounts (he got a hold of a block of cheese once). Our current dog, 7mos old shepherd-husky-whatever mix (a rescue of unknown provenance), is bonkers for cheese. He loves it. I don't give him a ton, but he gets up to 2T /day between his kong and occasional rewards and he doesn't have gas problems. I don't see any difference between days when he gets cream cheese in his kong and days when he gets peanut butter.
And my mother-in-law uses string cheese as a training reward with her golden retriever.