Workaround:

public class CustomRadDropDownList : RadDropDownList
{
    protected override RadDropDownListElement CreateDropDownListElement()
    {
        return new CustomRadDropDownListElement();
    }

    public override string ThemeClassName  
    { 
        get 
        { 
            return typeof(RadDropDownList).FullName;  
        }
    }
}

public class CustomRadDropDownListElement : RadDropDownListElement
{
    protected override RadDropDownListArrowButtonElement CreateArrowButtonElement()
    {
        return new CustomRadDropDownListArrowButtonElement();
    }

    protected override Type ThemeEffectiveType     
    { 
        get    
        { 
            return typeof(RadDropDownListElement);     
        }
    }
}

public class CustomRadDropDownListArrowButtonElement : RadDropDownListArrowButtonElement
{
    protected override Type ThemeEffectiveType     
    { 
        get    
        { 
            return typeof(RadDropDownListArrowButtonElement);     
        }
    }
    
    protected override void OnClick(EventArgs e)
    {
        MouseEventArgs args = e as MouseEventArgs;
        if (args.Button == System.Windows.Forms.MouseButtons.Left)
        {
            base.OnClick(e);
        }
    }
}