In a 2006 paper Bellare showed that HMAC remains secure even if collision resistance for MD5/SHA-1 is broken as long they are still PRFs.
The Wikipedia article on cryptographic hash functions mentions that
In practice, collision resistance is insufficient for many practical uses. In addition to collision resistance, it should be impossible for an adversary to find two messages with substantially similar digests; or to infer any useful information about the data, given only its digest. In particular, should behave as much as possible like a random function (often called a random oracle in proofs of security) while still being deterministic and efficiently computable.
It seems to me that in practice hash functions are usually considered to be PRFs. Is this valid and are commonly used compression functions all PRFs?
Note: The Bellare paper states
(There are to date no attacks that compromise the pseudorandomness of the compression functions of MD5 or SHA-1.)
Has this changed since then?
An interesting related paper by Kim et al., also from 2006, gives distinguishers for HMAC based on SHA-0 and HAVAL to distinguish it from HMAC with a random function. Which at least hints that it might be hard to determine if a compression function is a PRF.