Does BIP148 (UASF) offer any replay attack protection? Is there any protection against replay attacks in BIP148? 

Despite the popular name (UASF), it's effectively a hard fork (in the sense users with old nodes will be on a different chain), is there any protection against taking the transaction from the longer chain and putting it on "UASFCoin" chain, or vice versa? 

Something like Ethereum with EIP155 / chain ID.
No. BIP 148 is a soft fork as the BIP 148 chain is valid to all non-BIP148 nodes and can wipe out the non-BIP 148 chain if it were to be longer than it. Because it is a soft fork, there cannot be any replay protection otherwise it would become a hard fork.