OSR/NSR Tabletop Roleplaying Games

I think the main things to keep in mind is to remember that the factions' place in the world will always be defined by three things: their goals, their methods, and their history.

1. Their goals will bring them into conflict with other groups whose goals are at cross purposes, and will bring them positive associations with groups that share some similar aspirations. Are they trying to find a place to live? Well, someone already lives there. Are they trying to convert heathens? Those heathens probably already have their own religious organizations. Looking for resources? Maybe someone else is using them to harvest those resources in exchange for a cut. Etc.
2. A faction's methods can cause some division with other groups that sympathize with their goals but disagree with their methods or shared purpose with other groups that use related methods. Your hermits that use the lightning might be "good" but still abhorred by witch hunters. On the other hand, those "evil" blood mages that have been living underground for centuries might be inclined to help since they use similar magic, even though their goals might be unrelated.
3. A faction's history is easy: who helped them in the past and who hurt them. Grudges carry between generations really, really easily (look at Ireland, Palestine, or Native Americans), but so do memories of the groups who helped.

All this to say, when you start building the backstory of one group, their future goals, current methods, and past conflicts should make it pretty easy to see how their interactions can take shape. Just don't make anything too well aligned (or why are they even a separate faction) or too diametrically opposed (or it starts feeling contrived). History and relationships are messy, so your world's politics should be, too.