When setting IsEnabled to False, the DatePicker is still enabled and the dropdown/popup can be opened. Still the disabled style is applied as expected.

The issue occurs in all pickers

If you create an implicit style for DatePicker, for example, like this:

<Style TargetType="telerikInput:RadDatePicker">
    <Setter Property="SpinnerFormat" Value ="yyy/MMM/dd"/>
    <Setter Property="DisplayStringFormat" Value ="yyyy/MMM/dd"/>
    <Setter Property="IsClearButtonVisible" Value ="True"/>
    <Setter Property="IsToggleButtonVisible" Value ="True"/>
</Style>

an "object reference not set to an instance of an object" exception is raised.

As a temporary workaround, set the SpinnerFormat and DisplayStringFormat properties directly to the DatePicker instance.