Fate and free will are intertwined - get over it already!
Anyway.
Finrod chose to follow Fëanor to Middle Earth in the first place. His father returned to Valinor, but he (and his brothers and sister) did not. He was the one who brought a lot of "stuff" from Valinor...so he was probably a bit ambivalent about it.
After arriving...well, he chose to maintain his friendships with Fingon and Maedhros, and with Turgon, he took Ulmo's counsel. So, he was 'set up' in Nargothrond, but that is nobody's fault, per se.
Then, when Galadriel started nagging him about being single, he made the pronouncement about needing to remain free, because of an oath he would make. That statement was foresight, but it also meant he would accept that choice.
Barahir
saved his life, so without Barahir, he would have died earlier. He made that oath, perhaps knowing that it would be the very one to lead to his death.
None of that history can be forgotten when you consider the Tale of Tinúviel.
Thingol set the task, but when Beren came to Nargothrond, he met secretly with Finrod (well, behind closed doors). Finrod predicted that the sons of Fëanor would cause trouble, but he still chose to publically proclaim his plan to his people. He could have forsworn his oath in private, or promised Beren secret aid (not amounting to he himself going on the quest).
Making his intentions public was thus his own very concious choice - he knew what the ramifications would be, and he went through with it anyway, leaving with only a small band to assail Thangorodrim
It was not a suicide mission, but surely those who marched out of the gate of Nargothond expected never to return.
They made it as far as Minas Tirith on Tol Sirion, his own fortress, lost to Sauron by Orodreth (have we blamed him yet?)
And then they were captured by Sauron. And imprisoned. And killed.
I'd say the guilt rests squarely on Sauron's shoulders. He is the one who killed Finrod. In fact, he really killed all of Finrod's companions, and then Finrod sacrificed himself to save Beren at the last.
To take
one step back, we could say that Finrod would not have died if Lúthien and Huan had rescued Beren earlier. We don't know the exact timeline, but it was probably a matter of days, and maybe even hours. Thus, any delay on Lúthien's rescue attempt also contributed directly to Finrod's death.
Who to blame for that? Thingol (for imprisoning her in Hirilorn), and one step removed, Daeron for blabbing. But this still would not have cost Finrod his life, if Celegorm and Curufin had not imprisoned Lúthien and held her hostage. So....definately blame them for the delay!
But wait....the only way Lúthien could defeat Sauron, Lord of Werewolves, was with the help of Huan, loyal servant of the Fëanorions. No C/C, no Huan. So perhaps the only way she
could mount her rescue attempt successfully was in the way that she did.
So, if we're looking to cast blame, Finrod has much personal responsibility at stake - part of why we
for him is because he is so noble and self-sacrificing. He had chances to turn aside, only he didn't. He chose to be teh!coolest!elf!ever!, at the expense of even his own life. The cause of his death was the wolf, sent by Sauron. So, guilty party number one: Sauron. The biggest hinderance to Lúthien was C&C, so Celegorm and Curufin get second place. Thingol has much responsibility in the whole thing, though very little guilt - the only death he intended to cause was Beren's.
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