This is what I love about dogs. They really have no shame!
This is not an unusual behavior and I’ve dealt with it many times.
Any change in appetite could indicate a medical problem, such as a nutritional deficiency, so a visit to your veterinarian for a physical examination, and possibly blood work, would be prudent. However, I have rarely seen this indicate a medical problem; it is most likely a behavioral issue.
This could have developed for any number of behavioral reasons. Most likely, he could have discovered it recently and just likes the taste. It’s possible he used to be afraid of the cat and after becoming friends, he is now brave enough to enter the cat’s private territory. Some other household disruption could have incited it, such as the litter box becoming accessible, a spat occurred between them, or he stopped receiving other treats. You can think about whether these things have happened, but if they haven’t, it’s probably just a new taste that he has come to enjoy.
It is best to restrict the behavior. Cat feces has bacteria that could cause digestive upset and it can also carry parasites, the most common being one called giardia, that can transfer between them.
This is all very preventable with just a little strategic effort; so here are a couple ideas. Restrict access by moving the litter box. For example, install a cat entrance flap in the door leading to a utility room or place the box in a tight spot like behind a large appliance. Cover the liter box with a hood that the dog can’t fit through. Place the box on an elevated level that the cat can jump to but the dog can’t. If you can’t do this, you can get serious and use taste aversion. You could spray a few pieces of cat stool with bitter apply spray, but this is risky because the cat could be turned off by the odor and stop using the litter box. Hopefully one of these plans could work for you.
Good luck and in the meantime, I recommend avoiding any face licks from the dog!!
Dr. Clayton Greenway B. Sc DVM