Paranoia about our cat?

My sister, a first-time mom, recently brought her 4 month old over to our house. We have a cat who has never been outdoors and is healthy and up to date on vaccinations. But she insisted on keeping the cat away from the baby gear and toys. I've heard of pregnant women picking up diseases from handling cat litter, and obviously you can get infections from cat scratches, but is this a little excessive? Is there any kind of disease a baby can pick up from having a cat touch their stuff?

I don't think there is, but please correct me if I'm wrong. We're having a baby soon, and the cat has been lounging all over the place in their room, so obviously if I'm missing something, I want to know. NOT getting rid of the cat, but do I need to keep things cleaner or keep them away from the baby for a certain amount of time? But I have a feeling she's just a little paranoid. What do you all think?