This is due to lack of core capability in the wp customizer. To my knowledge, the customizer currently is only built to work with theme options, theme mods (widgets and menus). Hopefully post objects will come.
You might look at this. I haven’t used it but it appears to allow for ACF fields to be added to widgets in which can be manipulated via the customizer. https://gist.github.com/fabrizim/9c0f36365f20705f7f73
