You can respec anyone - including origin characters. Only two subclasses are locked for origin characters (Shadowheart?). Even if you respec Halsin he will still be a Druid. Same for the other Origins. It won't remove the tags.
Wyll and Shadowheart for sure. First, they are intimately tied to their sub-class; and second, they are the only ones that pick a sub-class at level one anyway.
