For anyone finding the way of using HeaderTemplate / ContentTemplate with CollectionContainer:
First Add Type Property in ViewModel
public Type Type { get { return this.GetType(); } }
Use Style.Triggers to set HeaderTemplate / ContentTemplate for the dynamic tabs identified by the Type property
<Window x:Class="TabDemo.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:TabDemo"
        xmlns:vm="clr-namespace:TabDemo.ViewModel"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="525"
        d:DataContext="{d:DesignInstance vm:TabViewModel}">
    <Window.Resources>
        <CollectionViewSource x:Key="ExistingTabs" Source="{Binding ExistingTabs}"/>
        <DataTemplate x:Key="TemplateForTheHeader" DataType="{x:Type vm:TabViewModel}">
            <TextBlock Text="{Binding Title}"/>
        </DataTemplate>
        <DataTemplate x:Key="TemplateForTheContent" DataType="{x:Type vm:TabViewModel}">
            <DockPanel>
                <DataGrid ItemsSource="{Binding Data}"></DataGrid>
            </DockPanel>
        </DataTemplate>
        <Style x:Key="TabItemStyle" TargetType="TabItem">
            <Style.Triggers>
                <DataTrigger Binding="{Binding Path=Type}" Value="{x:Type vm:TabViewModel}">
                    <Setter Property="HeaderTemplate" Value="{StaticResource TemplateForTheHeader}" />
                    <Setter Property="ContentTemplate" Value="{StaticResource TemplateForTheContent}" />
                </DataTrigger>
            </Style.Triggers>
        </Style>
    </Window.Resources>
    <Grid>
        <TabControl Grid.Row="1" ItemContainerStyle="{StaticResource TabItemStyle}">
            <TabControl.ItemsSource>
                <CompositeCollection>
                    <TabItem Header="Fixed Header">
                        <TabItem.Content>
                            <TextBlock Text="Fixed Content"/>
                        </TabItem.Content>
                    </TabItem>
                    <CollectionContainer Collection="{Binding Source={StaticResource ExistingTabs}}"/>
                </CompositeCollection>
            </TabControl.ItemsSource>
        </TabControl>
    </Grid>
</Window>
Referencing Anderson Imes's answer: https://stackoverflow.com/a/1348369/1196637