Most of that kind of conflict was usually framed in terms of human vs alien. Sometimes it was still within the federation (Worf trying to get someone to kill him when he was injured and likely wouldn't fully recover for example), but a lot of it was dealing with outsiders like humans having to deal with Ferengi who had very different ideology when it came to things like greed or women's rights.
For outsiders, while the show was pretty careful about expressing a respect for differing cultural views, they did seem to side one way or the other. When there was disagreement within the federation it tended to be a single person or small fraction with an unpopular opinion (like the guy who wanted to disassemble and reverse-engineer Data) creating conflict vs a sizable faction.