I don't know how Karelians in Finland view themselves but please bear in mind that if Karelians are indigenous then ethnic Finns & Estonians could be considered indigenous too since they are broadly part of the same ethnic group. They all speak a closely related language, share mythology and folklore.

To answer your question, most Karelians live in Russia which is outside the EU. It also appears that Karelians have a Finnish identity - even in Russia they are taught Finnish in schools. https://minorityrights.org/minorities/karelians/