If you have mental illness and it causes you to abuse or neglect the child, then you would be at risk. If you have TREATED mental illness that alleviates those symptoms and you have enough insight into your problem to ask for additional help if needed (for treatment), you would run a very low risk of losing custody.

Anyone can place an anonymous call to CPS about anything. Actually losing your child to them is a completely different thing.

An example from my own life, my next-door neighbor had a toddler. I found the toddler walking around on the 2nd floor of our building by herself in a diaper. I knew where she lived so when I took her next door, the door was open, no adult was in the apartment. I took the child into my apartment and called the police, CPS was also called and about an hour later the mother showed up, had gone to the store and left the girl at home asleep by herself. She must have opened the door herself and walked out.

CPS did not remove the child, although they should have. They did come back to make visits periodically.