For me it turned out that the plugin Contact Form 7 – PayPal Add-on Version 1.3.4 was breaking the Datepicker functionality.
Disabling this plugin made Datepicker Version 2.5.2 with Contact Form 7 version 4.4.1 work as expected on WordPress 4.5.
(Not sure if this is the same reason it doesn’t work for mlmn, so therefore not setting this issue to Resolved, although it is resolved for me now).