This is a weird bug that just came up recently on multiple installations I have set up. When I click ‘Publish’ on custom post types using ACF Pro fields, it loads for a moment, and then jumps to the default WordPress Posts listing. If I use ACF fields on normal posts, they work. If I disable the ACF fields on the custom posts, they work. It’s only when I use them together that I get this issue. It also adds ‘wp-post-new-reload=true’ to the url twice for some reason.
Never mind. I don’t know how, but this seemed to solve itself.