How compatible are mammalian digestive systems?
I think this would depend entirely on the diet of the host and donor mammal.

Assuming they are of similar size and diet, I don't see any reason why this wouldn't work. The gut tends to absorb more or less everything in the food.

If the diet of the two mammals differed significantly, I could see some problems with eating the correct foods. Herbivores with the significantly shorter carnivore gut would have trouble killing and eating things without carnivore teeth/claws/what have you, and the plants would not provide enough nutrition on their own. Rabbits, for instance, have a two-pass digestive system, so in order to use a rabbit gut the mammal would have to eat their own feces regularly. (Rabbits have digestive bacteria in their colon, but grass has to travel to the colon and then back 'upstream' to the absorptive part of the gut. So this is achieved by going around again.)