I saw that some people did leave their things, but the immense majority take them. I leave my things at local parks, but at Disney I did not feel safe doing so. I don’t mean that it is too bad, just that I felt like it could happen there. I read of some people that had things stolen from their diaper bags, again nothing major but still a big bummer. By the way, not all stroller areas are the same. Some seem safer than others.
As a side: do you know about the hamster packs? (Search for “Hamster Stroller Bags” on Amazon). This could solve your problem. You can carry most things on them, you can get a lock of some sort for the zipper, something easy for you to open. Then you can bring a small bag just for the valuables (phones, camera, wallet etc.) Next time I go to Disney this is what I intend to bring.
I should add that when I went we did not have to carry any coats or blankets like Tate. If I had, I would probably leave those, as they are way too cumbersome to carry. We only carried 1 diaper bag, nothing else.