In ST:TNG Season 5, episode 3 (Ensign Ro), the following scene occurs:
[Transporter room]
(a young woman in red uniform beams in, wearing a sullen expression and a fancy earring)
RO: Ensign Ro Laren reporting as ordered, Commander.
RIKER: You will follow Starfleet uniform code aboard this ship, Ensign.
(she removes the earring)
Why, when Worf is permitted to wear his sash, is Ro not allowed to wear her earpiece?
Fairly simple: Worf is a respected officer with a spotless record, thus he gets a bit more tolerance in some areas. Ro was court-martialed and had to be sprung out of prison by an admiral, therefore Riker has her toe the line like a first-year cadet. She was out of uniform upon arrival, and got snapped at for it.
In reality, Worf was wearing the sash in Encounter at Farpoint and they just never had a reason to take it off. Ro needed to be pictured as rather less desirable, and a reprimand from the FO 15 seconds after arrival does that quite well.
According to the Memory Alpha article on Starfleet Uniform Code, it is explained that there seem to be some inconsistencies regarding Bajoran earings. Although, as the OP points out, Worf was able to wear his baldric, this may have been because it denotes the symbol of a Klingon's house, according to this article, which is highly significant to a Klingon. (Note I'm not saying that the Bajoran earing isn't important to Bajorans, but it may have been due to cultural understandings between the Federation and Bajorans at the time not being fully developed; indeed apparently one Bajoran serving on the Enterprise-E wore an earing according to the Memory Alpha article which suggests to me that there may have been improved cultural understandings between the Bajorans and Federation, especially following the events of Star Trek: Deep Space 9).
To explain why Riker said this, I do point out that Starfleet Uniform code does specify that:
elaborate headbands and jewelry were in violation of the dress code
hence, perhaps we can conclude that Riker saw Ro's earing as an 'elaborate piece of jewelry' so on that basis asked her to remove it.
Similarly, in VOY 'Learning Curve', Tuvok requires that Gerron removes his Bajoran earing as well. This suggests that the earing is indeed seen as an 'elaborate piece of jewelry', like Chell's Kazleti pendant. This probably reflects Starfleet's lack of understanding of Bajoran customs. Considering the Federation sets up on Deep Space Nine in 2370 and the USS Voyager is lost in the Delta Quadrant in 2371, over a year Starfleet may have not had time to update their protocols to accept Bajoran earings.
Because she hadn't obtained permission yet.
At the end of that very same episode, she asks Picard for permission to continue wearing her earring, and he grants it.
Since Worf is already wearing his baldric when we first see him, it's reasonable to assume that he has already asked for and been given an exemption that allows him to wear it.
In Memory Alpha, it states that if someone wants to wear anything not part of the dress code, they need the captain's permission to wear it. Worf probably already obtained permission, whereas Ro obviously had not.
I always thought it was because the boldric is tightly put on the uniform and made for someone in combat, while the earings are not fit for combat given they hang down and could be easily pulled out or used to control the wearer in hand to hand. So basically the boldric either worf was trained to wear in combat or was made to not be used against him unlike a big easy to grab earing.
Also for those who say it was starfleet just not understanding bajoran culture should remember when kira was given a field commission she had to take her earing off and that was like the last few episodes of ds9, this might also mean it is up to the commander if the posting has enough combat for it to matter or not.
This isn't canon, but there is some flexibility in military uniforms. There are several options that may or may not be worn depending on the occasion. Ribbons, medals, and other insignia can be optional; e.g., a surface warfare pin should be worn by a qualified sailor but it's not wrong to leave it off. Worf's sash seems to fall into that category.
There is not to say that there are many options. You must be in proper uniform while on duty unless ordered otherwise. Rank insignia must always be displayed with rare exceptions. You must wear a cover (hat/cap) outside unless the area is designated a no-cover zone.
I don't think the ear piece is religious, in DS9 its described as representing their 'D'jarra' (the class of worker they were born into 'preoccupation by the Cardassions'). It may be a sign they trust the Prophets but that's not its intended purpose
On the other hand Worf wore a representation to his house, the 2nd most important thing in Klingon culture (next to honor)
Therefore one is a strongly acceptable compromise (for the only Klingon in star-fleet, where relations with that culture aren't the best most of the time). Whereas the other wants to wear an ear piece that has no significant meaning anymore to her culture. Relations with Bajor suggested that others in that species were OK with removing it without offence
It stands to reason that the only pure Klingon in star-fleet would be allowed to show his house (as star-fleets would like more Klingons to join), and the Bajorans who have shown no cultural problem by taking them off, would be considered jewelry.
