I do not recommend allowing your cat to go into your refrigerator. Not only is it unhygienic, but it could be unsafe for kitty if you forget about him and leave him in the fridge.
My male cat likes to bite bags. He knows there are bags in the fridge, so he usually runs to the fridge every time we open the door. It is annoying. There was one time that he jumped into the fridge and we did not notice. About 10 minutes later, we heard him meowing and realized he was trapped in the fridge.
Here’s a video of a cat in a refrigerator:
I’m not sure why this cat’s owner decided to place kitty in the fridge, but I sure hope they are careful to ensure kitty stays healthy and safe!