Apparently ACF Pro makes the Toolset Access plugin to not work properly. It seems that ACF Pro is somehow changing the z-index of the TinyMCE or the div.ui-widget-overlay.ui-front and the result is an overlapping of modal windows. Please see the image here: https://d7j863fr5jhrr.cloudfront.net/wp-content/uploads/2017/05/525636-Screen_Shot_2017_05_18_at_4.30.19_PM.png
I understand you don’t support or debug third party plugins but disabling ACF Pro the issue disappears.
Please open a new support ticket at https://support.advancedcustomfields.com/new-ticket/ so that this issue can be escalated to the developer.