Pine (and cedar) shavings aren’t immediately toxic, so that may be where some of the misinformation is coming from. The problem with pine shavings (and why they aren’t safe) is the phenols that they contain. Phenols accumulate in the body when bunnies are exposed to them for long periods of time (e.g. having pine shavings for litter). Phenols mess with the liver enzymes, essentially causing them to be overproduced. But bunnies don’t simply drop dead from this. It is more of an issue if they suddenly need surgery because it causes problems with anesthesia. It also interferes with some other medications like opiods. This is why pine shavings are considered to be unsafe. There are some suspicion of there being a link to cancer as well, but so far there isn’t enough evidence.
Paper-based litters such as CareFresh and Yesterdays News are popular. Pine pellets like Feline Pine or horse stall pellets are safe because they are kiln dried and do not contain phenols. Some people also use wood stove pellets, which are cheap. However, where I live, they are not available year round.