Tobi being Obito is.....

[Totsuka No Tsurugi]

Yes it might've been the trigger for why he turned the way he did but to say its why he started the war is not true atleast not.fully. Yahiko was the reason Nagato turned so what's wrong with Rin being Obito's? Obito and Nagato weren't true villains I see them more as antagonists they were truly never evil they were just manipulated/influenced so it was possible for both to be talked to the good side. That's your opinion on how he was handled in the kaguya fight but I respect it I liked the way he was handled.

Yahiko and Nagato case is different with Obito and Rin, in Nagato case they created a whole backstory for him, explaining every detail of what went wrong,
Yahiko was Nagato's friend/leader and family, they've been through so much hardship, in the end they were betrayed by hanzo and it leads to Yahiko's death.... Nagato's reason is justified i mean after all that work that's how it ended ? of course he snapped, while Obito's reason is pretty much over a girl and his "Other Reason" was never fully explained,

There's also the fact that Obito let Madara Manipulate/influence himself while Nagato never realized that till the end,
the moment they revealed that Tobi is Obito i know that this idiot will get TNJed, there goes the suspense.