So if you have an address with coins in it that uses an uncompressed public key (preceeded by a "04") then how can coins from that wallet be utilized with a network that doesn't allow such public keys? Compressing the public key changes the relevant wallet address and would prevent one from being able to access one's coins at that point. Does bitcoin still allow the "04"? I've read, it seems, that bitcoin cash does not.
Uncompressed keys are only disallowed for segwit output types. Since segwit outputs are a completely new type of output that requires new addresses (and a new address type eventually), there won't be any effect on your current addresses and keys. Non-segwit transactions and outputs can still exist and will happen. These transactions will work in the exact same way they do now; you won't be using segwit (and thus not allowed to use uncompressed keys) unless you explicitly go to use it.
Bitcoin Cash does not have segwit, so they are not invalidating uncompressed keys. The only part of BIP 143 that Bitcoin Cash is using is the sighashing algorithm.