I'm a practicing Germanic Polytheist and I'll tell you some main characteristics among Indigenous Heathens(using this term to refer to anyone practicing a polytheistic faith related to the people of the Northern European Germanic tribes, such as Asatru, Heathenry, Teutonic Animism, Vanatru etc.).
1) We are ancestral. The majority of us revere the ancestors very highly, and in some cases regard them as minor deities. In other cases they play a role similarly to how the Christian saints and angels play a role in the cosmos, as they are the go between among the living and the divine.
2) We honor nature. There are two, sometimes three (if you include The Giants) tribes of gods, one of them being the Vanir, which are gods of nature, fertility and procreation. Some most notable deities are Frey, Freya, Njord and Nerthus. In my personal opinion (some would disagree) they can be compared to as being similar to various gods in the Hellenic pantheon, such as Dionysus, Poseidon, Pan, Apollo and Artemis. There are also various nature and land spirits called Alfar, or in English, elves or elven.
3) We strive to be honorable and strong. The second tribe of gods are the Aesir. These are gods of courage, strength, war, honor, intelligence, and pretty much all things that a human should strive to be. This is where the most famous gods, such as Thor, Odin, Frigga and Tyr, are from. Again in my opinion they can be compared to the Greek Olympians or some Kemetic gods, including Isis, Osiris and Horus.
There are however a few differences and some conflicts within the heathen community, that divides us into a few different communities.
1) Not all of us regard The Giants (or Jotunnar) as gods. Most definitely revere giantesses such as Jord as deities, but some like Ymir, or Hel and Loki (which are in the tribe of Aesir by adoption) are actually viewed negatively by most heathens, because Loki is most known as being a trickster god and Hel is a goddess of death, which can frighten some people. Personally I view them as gods of primordial, and possibly chaotic forces in The Universe, but a necessary part of life and the natural world. Most Giants are widely regarded, at least by anthropologists and archaeologists as being cognate with the Greek Titans.
2) There is an ongoing debate regarding "folkish spirituality" and "universalist". The core Asatru community, especially the Asatru Folk Assembly, believe that just as Native American spiritualities reserve the right to not permit people to practice in their circles who aren't Native American or how Shinto Circles also reserve that right regarding people of non-Japanese ethnicity, Northern Europeans should have that right too. The problem is that whenever white people exclude brown people, no matter what they say, it reminds society of years and years of slavery, genocide and segregation.
The belief behind this is about identity and harkening back to one's roots. You don't choose a religion based on "it makes me feel good", which isn't based on hundreds of years of ancestry, culture, religion and people living, fighting and dying. You don't choose a faith, you HAVE an identity.
Then there are the Universalists who believe that anyone of any race can worship any god from any culture. These groups are groups such as The Troth. You'll find Northern European, West African, and a mix of different ethnicities in these circles.
Personally I find myself somewhere in between. On one hand I do believe that everyone has an indigenous identity and heritage, and you should honor that. On the other hand I do also believe that all ancient indigenous cultures were believing and practicing similar practices, and the only differences were slightly varying lore, different language and cultural practices.
So that's Heathenry summed up in a few paragraphs.
