Sorry Ec, but there I must take issue.

It is true that among the many kinds of mice around the world some really are specialist eaters of seeds or bulbs, but typically even such are only too happy for the occasional fat-and-protein-rich treat if it comes their way, as many a grasshopper or mealworm has found out the hard way. There is nothing unusual about this; most animals will relish an exotic food that presents the right gustatory and olfactory (and often visual) stimuli.

Just for example, where do you suppose our hunter-gatherer ancestors would have acquired their taste for say, bacon or chocolate? 

Also, many mice are carnivores for choice, their main diets being invertebrates or lizards, though I do not offhand know of any actual specialists. I suspect that most or all of them would happily benefit from the occasional vegetable treat of fruit or nuts, say.

More to the point, the mice in question in this discussion probably are house mice, and house mice are notoriously omnivorous. I guarantee that a sufficiently hungry house mouse would gorge on cheese of any kind, given the chance and no choice of diet. I furthermore guarantee that some cheeses would attract any house mouse, though I have no idea what was proffered in this example.

Just for one live anecdote concerning murine carnivory, a student friend of mine had a cage of domestic mice, and any time he caught one of our local large garden grasshoppers, which have huge, spiky, painfully kicking hind legs, he would release it into their cage. He had to be quick; the mice went mad; some of them would be kicked right across the cage, but bounced right back, and no grasshopper survived for more than a minute or so. Conversely, I have seen naive mice screw up their eyes and retreat hastily at the mere smell of a far smaller, more inoffensive grasshopper if their first experience of such a delicacy had been a kick on an investigative nose.