We only have dogs, but we leave a huge auto-filling water dish for our two dogs to drink whenever they'd like - they need access to water at all times. My little ones are 10 months and 2 years old, and I've never blocked off the dog water. It is dangerous - it isn't just an issue of getting wet, but they could go face-down in the water and drown. So, it was absolutely necessary that the kids were taught the first time they went anywhere near it not to GO near it. It's in our kitchen, where the kids are not allowed to go unsupervised, and they know it. However, even if they're in the kitchen with me while I'm cooking dinner, the water is there, and they could go splash in it if they wanted to.
It's a NO zone. My toddler has known since he was 8 months old that the dog water is off limits. My baby started crawling 3 months ago but didn't go near the water dish until 3-4 weeks ago. If he goes near it, I tell him firmly, "No!" and I move him away from the water. If he goes back to it, I do it again. "No!" and remove him from the situation. He already knows that it's a NO zone, to go into the kitchen unsupervised, and he doesn't test me because I'll just move him anyway. But when we are in the kitchen and he doesn't think I'm watching, he will sometimes start looking at the water and slowly going towards it, looking at the water, then back at me, then back at the water... I will go back to the basics when this happens: Tell him "No!" and move him away from the water dish. He knows - they catch on quickly.
Of course the best way to keep a baby out of anything is to keep an eye on them, but sometimes we just need to go grab something from another room or take our eyes off of our baby for "just 1 second". So, either the NO zone is really concreted into their sneaky little brains... or we use gates...
If the cat can't make it to the litter box, you're in trouble. Haha. So, yes, I understand that a gate at that door is impossible in your situation. Perhaps there's another place where you can put a gate? I don't know the layout of your home, but at my sister's home, the bathroom and bedrooms are all in one cluster, separated from the family room and dining room by a little hallway - that hallway gets gated off, and the baby is free to roam around the living and dining rooms. Maybe you could block off whatever area has the open closet/cat area while providing enough room for the cat to land after jumping over the gate?