It's simple — refer to people by what they want to be known as.

• indigenous peoples of the Arctic and Subarctic
  • Alaska Native peoples
  • Eskimo is often seen as offensive [2], instead use Inuit and/or Yupik
• disabled is not a dirty word [2] [3]
  • person-first language versus identity-first language (although this document was produced by a university, it comports with many other similar documents [bio] produced by the in-group)
• for indigenous people of the Americas:
  • Indian isn't really accurate, because that's a historical mistake. (see also: the origin of the term West Indies)
  • I've heard some indigenous people say that American is inaccurate as well, as that name was chosen by Europeans. The Americas were named after the Italian explorer Amerigo Vespucci.
  • I've seen some indigenous people say that Native and Indigenous are better options [2]
  • As always, people aren't a monolith and there is never unanimity among any marginalized population, especially across tribes or across generations. So you may see older indigenous people referring to themselves in ways that younger people might not.
• Romani people
  • Some Roma consider gypsy to be a slur [2] [3] [4]. Certainly gyp should be avoided.
• homeless folks — I've seen suggestions by the out-group that alternatives like houseless, unsheltered, or unhoused might be better. However, when looking at resources created by actual homeless people, it seems like homeless is used fairly frequently. This could be similar to the issue with disabled not being a dirty word, or it could be because it's harder for homeless people to gather in community spaces to advocate for themselves as effectively as other groups do, I'm not sure.
  • Caveats — I haven't seen an "overall summary" produced by an in-group person, so there's the big caveat that the above is my own personal (out-group) summary. Also, while I've spent several hours reading/watching homeless-produced content, I'm sure there are other people out there who have more experience with this.

† In linguistics and geopolitics, an exonym is a name of a place or group that's chosen by outsiders, and an endonym is a name chosen by insiders. For example, compare Mount McKinley to Denali.

‡ An in-group is a group that someone psychologically identifies with, and an out-group is one that someone doesn't identify with.