"The Sindar" are not a singular group with a coherent leadership structure and unified political goals. Specifically, Thingol's priorities, grudges, etc cannot be assumed to be accurate for all of the Sindar, despite the overwhelming presence he has in the Silmarillion.
The Falathrim, under Cirdan, are nominally Thingol's vassals, but notably act independently to build friendships with the Noldor. Cirdan swore friendship to the Noldor at the Mereth Aderthad; gave military aid to Fingon during the 2nd attack on Hithlum; is very close to Finrod, who also built him a watchtower; and by the end of the 1st age, when he is on Balar, is notably not Elwing's vassal. From then through the end of the 2nd Age is primarily associated with Gil-Galad, a Noldorin king.
The green-elves, per Tolkien's notes and IMO a lot of in-text evidence, are not Thingol's vassals but a separate but allied kingdom and people with what appears to be complex internal politics. After the death of Denethor, they refuse to name another king and pull back from the war against Morgoth, but some green-elves live within Thingol's realm (Saeros; the guest-elves). Beren and Luthien live in Ossiriand after the Silmaril quest, and Dior (in some continuities) marries a green-elf; additionally, Beren and Dior rally an army of green-elves to defeat the dwarvish army that sacked Menegroth. However, the green-elves are not noted as participating in the defense of Doriath during the 2nd Kinslaying (the precise date of which may have taken Dior by surprise, but considering his ongoing correspondence with the Sons of Fëanor regarding the Silmaril was not exactly unforseeable). The sons of Feanor are strongly implied to also have a consistently decent relationship with the green-elves, including after the 2nd Kinslaying. Strong factionalism or politically independent clans seem likely.
The Northern Sindar are shunned by Thingol for possibly having fallen under the sway of Mordor; some go east with the Sons of Fëanor while some remain in Mithrim as vassals of Fingolfin (and, depending on the continuity, Turgon). Northern Sindar probably made up a significant portion of the Fëanorian forces in particular, which were presumably more-or-less in line with Fëanorian policy until the noted rebellions at the 3rd Kinslaying-- that is, through both deeds of surpassing valor during the Bragollach and the 2nd Kinslaying (it's possible that some portion of Celegorm's "cruel servants" were of the Northern Sindar).