1) Worf is different, because he's a member of Starfleet.
Take Nog, for example. In Ferengi culture, it might be perfectly respectable, even laudable, to cheat on a business deal (with a non-Ferengi, at least). But if he was negotiating a settlement and went back on his side after the Federation got what they wanted, he'd be punished, not because they don't (officially) respect Ferengi culture, but because he's representing Starfleet.
Worf is a member of the Federation and bound by Federation laws. So if he kills someone to restore their honor, that's still murder by the Federation law. Even if he resigned his commission temporarily, he's still a citizen of the Federation which may well have certain rules.
From "Sons of Mogh":
WORF: Captain, I do not have an answer. Sir, I realise my actions were in violation of Starfleet regulations, but
SISKO: Regulations? We're not talking about some obscure technicality, Mister Worf. You tried to commit premeditated murder.
DAX: Benjamin, it wasn't murder. Worf and Kurn were performing a Mauk-to'Vor ritual. It's part of Klingon belief that when
SISKO: At the moment, I don't give a damn about Klingon beliefs, rituals or custom. Now I have given you both a lot of leeway when it comes to following Klingon traditions, but in case you haven't noticed, this is not a Klingon station, and those are not Klingon uniforms you're wearing. There is a limit to how far I'll go to accommodate cultural diversity among my officers and you've just reached it. When your brother is released from the infirmary, you better find another way to settle your family problems. Is that clear?
2) Where everybody involved is willing, and not in Starfleet, generally speaking the Federation will not intervene. When it's a single culture, they may well not intervene no matter what unless there's a formal request for asylum.
This is the case in "Half a Life," and in many other episodes focused on the Prime Directive... yes, the culture might be unfair, but everyone involved is part of it and okay with it. Even if it was absolutely forced (a death squad kills you when you hit 40), the Federation might disapprove, might withdraw contact, but would not interfere with their internal affairs any more than they would if a convicted prisoner was about to be executed (which some might feel is equally abhorrent)... at least, unless someone is asking formally for asylum. It then potentially becomes a diplomatic mess, but they have an opportunity to interfere.
If multiple cultures are involved, or it takes place on Federation property, it's another matter. The Federation would probably intervene if, say, a Klingon attempted to enforce a Klingon ritual which made legal lethal retribution because of the actions of a non-Federation Tellarite (I'm using them because they hardly ever get mentioned) who offended them in some way. Within Klingon culture, that might be the way they did things, but once it crosses the boundaries, it's a diplomatic incident. Yet, if the Tellarite was really fond of Klingon culture and respected an honorable death for some reason from some Klingons on a non-Federation world, they probably wouldn't interfere (though friends and family might, see below).
3) People always care more when their friends are involved.
If I encountered a culture where say everyone was randomly selected a partner that they must marry, and everyone's okay with it, nobody's forced except for some social consequences, I'd respect that culture. But if my friend was randomly selected to go to their mate, and I KNOW that they're miserable, that they really love someone else, even if they're "willing" because that's what their culture says they must do, then I'm more likely to speak up, say something about how stupid the tradition is, even if it's not officially Federation policy. Even more when death is involved, like in "Ethics" when Worf felt he might need to commit suicide.
It also goes the other way... there may be times where, in following a Klingon tradition, Worf violated Starfleet regs/Federation law in a way that should cost him his freedom or career, but because they know him, his superior officers didn't make a big deal out of it.
Dax, sort of played both sides in "Sons of Mogh", she tried to stop the killing of Worf's brother, but then defended the practice before Sisko, because she abstractly respects the culture, but when someone she cares about and knows is involved, she didn't want to let it happen, she knew it would affect him negatively the rest of his life.