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.
I sort of thought that was the whole point of the show: the humans live in a liberal utopia according to western progressives and the aliens are everyone else in the world they have to get along with.
It let the writers comment on contemporary issues with adjustable knobs for violence, sex, and laser beams, in hopes that the right cocktail could dislodge people from from their instinctive association with a political identity and let them learn something.
It seems to me the assumption of consensus with disagreement coming from small fringe factions mirrored much of the American experience during the TNG era.
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.