I think Snoop saw what's coming and clearly was not having any of that, so he prioritized himself. He wanted to be on acceptable terms with Suge and Puffy, at least acceptable enough not to get killed by either. I think he was scared shitless and pussied out - when you think about it, if Puffy wanted to retaliate for Biggie in revenge again, Snoop thought he could have been the next target if he stood with his boys, as he was the second-largest star at Death Row. I think he was scared of that, maybe one of the reasons so many big artists left Death Row at that time. Dre probably left because he could tell drama is coming and he wanted none of that as well.
Another thing was that Bad Boy was running with crips, which Snoop claimed at the time, despite the fact he was simply paying them for the right to claim. Death Row had a reputation to uphold and affiliated themselves with bloods.