Is it safe to let our cat sleep with our baby?

No. A 7 month old baby will likely poke at or grab a part of the cat, neither of which will make the cat happy. Parents should constantly watch the baby if any pets are nearby. A dog or cat will likely sniff a baby to remember the baby's scent, and to find out what is going on, just out of curiosity. Other types of pets should probably stay away from babies.
No. A pet in the crib is just not a good idea. They are a sids risk, and have the potential of scratching or biting the baby if accidentally grabbed or rolled on. However, this is not "lady and the tramp", and cats do not intentionally suffocate children, that's an urban legend. So do not encourage the cat to go in there, but if it does happen, it's not a desperate emergency.
No. It is dangerous to let your cat sleep with your baby for several reasons. Cats can get jealous, just like small children, and may exhibit behaviors which are out of character. Cats can carry germs which may make your baby sick. Your cat may smother the baby without even realizing it.