At the moment, there is always an active tab. I have logged the idea to allow for no tabs selection and you can Follow it here: https://feedback.telerik.com/blazor/1435948-allow-tabstrip-with-no-active-tabs.
On a header template - this feature request already exists and you can Follow it (I added your vote) here: https://feedback.telerik.com/blazor/1419293-tab-strip-label-template.
In the meantime, you can hide all the contents inside the tab in order to mimic closing it.
UI for Blazor