All cheeses including cream cheese should never be left out at room temperature overnight or more than a few hours.
It's okay to leave the cream cheese out for a few hours if you plan to use or eat the cream cheese within those 2 hours but if you're not gonna eat or use the cream cheese within 2 hours you should place it in the refrigerator.
If you leave the cream cheese out overnight or longer than a few hours it can grow E. Coli or other bacteria in the cheese and make you sick.
Also maggots could get into the cream cheese as it's happened to me before when I got distracted by something else and accidentally left part of a cream cheese package out overnight and by morning there were maggots in the cream cheese.
So always refrigerate the cream cheese if not eating or using it.