Okay, so kariginu is basically what court nobles back then would normally wear. A Touhou instance would be Okina. Note that kariginu used in the context of Shintō rituals would be "Jōe". On the other hand, strictly speaking, it has to be pure white without patterns to count as one, so there is still wiggle room to make the relation based on the general definition of the garment to assume that the Hakurei clan is nobility – i.e. it might not be Hakurei Reimu, but Hakurei no Reimu, if it's a honsei.
As for hitoe, a hitoe kimono means it's unlined – it's just one layer of fabric. And hakama is, of course, those big trousers we have probably seen in other media such as with shrine maidens and school martial arts club.
