The problem in Android 5.0 is the "mode" which determines whether to use a calendar or not is read at construct time, and in code you can't set the mode until after it has been constructed, thus it's too late. (Source is here: DatePicker Source Code)
My solution was to create my own reusable DatePicker layout that specifies the "no calendar" mode, and construct my DateTimes programmatically with that layout instead of Android's default.
Bottom line is, create a "DatePicker.axml" file, put it in the resources folder, and paste the following as its contents:
<?xml version="1.0" encoding="utf-8"?>
<DatePicker xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
android:calendarViewShown="false"
android:datePickerMode="spinner"/>
and declare it wherever you need in code like this:
LayoutInflater inflater = LayoutInflater.From( Activity );
DatePicker datePicker = (DatePicker)inflater.Inflate( Resource.Layout.DatePicker, null );