I think it's interesting how many people worry about factorization. A second preimage attack on SHA2 would be at least as dangerous, and nowhere near as many people know or care about its assumptions.
SHA-2 was on related shaky ground. Remember that in relatively short significant advances were made in breaking MD-5 and SHA-1. SHA-2 is based on similar constructs as MD-5/SHA-1.
For this reason the SHA-3 competition was started to find a new hash function based on different principles.
In the end it was found that creating practical attacks for SHA-2 is too hard. But we don't know what the future will bring.
The difference between RSA and SHA-2 is that RSA is a very nice mathematical structure and we are still learning a lot about (prime) numbers. In contrast, SHA-2 is weird structure that has to solve a hard problem. It is hard to attack.
