Just to be clear, you're hashing a 64-bit value into a 32-bit one. Also, a good hash function will produce an even distribution of values (for hopefully obvious reasons!).
You could ignore half the bits, but that would leave you with half the possible values producing one single. So, you want to take all the bits into account somehow when producing the hashcode.
Options for mashing the bits together are: AND, OR, XOR. If you think about it, AND and OR aren't going to produce an even distribution of values at all. XOR does, so it's the only good choice.