In WPF can you filter a CollectionViewSource without code behind?

You can do pretty much anything in XAML if you “try hard enough”, up to writing whole programs in it.

You will never get around code behind (well, if you use libraries you don’t have to write any but the application still relies on it of course), here’s an example of what you can do in this specific case:

<CollectionViewSource x:Key="Filtered" Source="{Binding DpData}"
                      xmlns:me="clr-namespace:Test.MarkupExtensions">
    <CollectionViewSource.Filter>
        <me:Filter>
            <me:PropertyFilter PropertyName="Name" Value="Skeet" />
        </me:Filter>
    </CollectionViewSource.Filter>
</CollectionViewSource>

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows.Markup;
using System.Windows.Data;
using System.Collections.ObjectModel;
using System.Windows;
using System.Text.RegularExpressions;

namespace Test.MarkupExtensions
{
    [ContentProperty("Filters")]
    class FilterExtension : MarkupExtension
    {
        private readonly Collection<IFilter> _filters = new Collection<IFilter>();
        public ICollection<IFilter> Filters { get { return _filters; } }

        public override object ProvideValue(IServiceProvider serviceProvider)
        {
            return new FilterEventHandler((s, e) =>
                {
                    foreach (var filter in Filters)
                    {
                        var res = filter.Filter(e.Item);
                        if (!res)
                        {
                            e.Accepted = false;
                            return;
                        }
                    }
                    e.Accepted = true;
                });
        }
    }

    public interface IFilter
    {
        bool Filter(object item);
    }

    // Sketchy Example Filter
    public class PropertyFilter : DependencyObject, IFilter
    {
        public static readonly DependencyProperty PropertyNameProperty =
            DependencyProperty.Register("PropertyName", typeof(string), typeof(PropertyFilter), new UIPropertyMetadata(null));
        public string PropertyName
        {
            get { return (string)GetValue(PropertyNameProperty); }
            set { SetValue(PropertyNameProperty, value); }
        }
        public static readonly DependencyProperty ValueProperty =
            DependencyProperty.Register("Value", typeof(object), typeof(PropertyFilter), new UIPropertyMetadata(null));
        public object Value
        {
            get { return (object)GetValue(ValueProperty); }
            set { SetValue(ValueProperty, value); }
        }
        public static readonly DependencyProperty RegexPatternProperty =
            DependencyProperty.Register("RegexPattern", typeof(string), typeof(PropertyFilter), new UIPropertyMetadata(null));
        public string RegexPattern
        {
            get { return (string)GetValue(RegexPatternProperty); }
            set { SetValue(RegexPatternProperty, value); }
        }

        public bool Filter(object item)
        {
            var type = item.GetType();
            var itemValue = type.GetProperty(PropertyName).GetValue(item, null);
            if (RegexPattern == null)
            {
                return (object.Equals(itemValue, Value));
            }
            else
            {
                if (itemValue is string == false)
                {
                    throw new Exception("Cannot match non-string with regex.");
                }
                else
                {
                    return Regex.Match((string)itemValue, RegexPattern).Success;
                }
            }
        }
    }
}

Markup extensions are your friend if you want to do something in XAML.

(You might want to spell out the name of the extension, i.e. me:FilterExtension as the on-the-fly checking in Visual Studio may complain without reason, it still compiles and runs of course but the warnings might be annoying.
Also do not expect the CollectionViewSource.Filter to show up in the IntelliSense, it does not expect you to set that handler via XML-element-notation)