I think it is very different to other indigenous people, in many important ways.
Sámi and Germanic speaking peoples have lived side by side for almost 2000 years. That's very different from the classical colonial story.
For much of history, Sámi were exploited but prized subjects, because they were taxed in furs, a very profitable trade commodity. At one point, three states (Norway, Sweden and Russia) taxed the Sámi... although that can't have been fun for the Sámi, it also gave them considerable legal protection, since you didn't mess with someone that profitable.
Assimilation is also a complex story. It was worst in Norway in the 20th century - after WW2, which makes it especially damning. There they committed basically all the classic colonial crimes that e.g. Canada and Australia committed against their indigenous populations - separation of families, suppression of language, forced sterilization, you name it.
But at other times, especially in Sweden, they went to the other extreme of segregation instead, under the "Lapp ska vara lapp" policy, where Sami were not allowed to get education, and those who failed to live up to the exotisized image (e.g. by not being reindeer herders) were denied traditional rights.
On religion, it's also rather far from the classic "they came and imposed their religion on us" story. Christianity didn't reach the Sámi much later than it reached the Norse, if it was later at all. The first chapel in Finnmark was apparently built by Sami. The presence of the Virgin Mary in some Sámi folk tales is good evidence that it wasn't after the reformation the Sámi became Christian. However, since the Sámi were at that time nomadic, had low literacy rates and lived geographically and culturally far from ecclesiastical overview, they did not stay orthodox and mixed in a lot of animistic beliefs and superstitions with their Christianity. Sápmi today is a stronghold of arch-conservative Christianity, in particular followers of the 19th century Sámi pietist reformer Lars Levi Læstadius, and that's another thing that doesn't fit well with the Sámi as a "typical indigenous people", as well as a source of conflict between generations, where younger Sámi people may be a lot more OK with the idea of themselves as basically pagan (and their pietist parent generation as self-hating colonialism victims).
So, let's be careful to not squeeze the Sámi into a generic indigenous people mold. I get that doing so is often a well-meaning effort to justify Sámi rights, but it should not be necessary to cut the foot to make that shoe fit. I think it's important to focus on the value of language and culture over ancestry.