Wikipedia, the one true source of knowledge, states:
On most older microprocessors, bitwise operations are slightly faster than addition and subtraction operations and usually significantly faster than multiplication and division operations. On modern architectures, this is not the case: bitwise operations are generally the same speed as addition (though still faster than multiplication).
Is there a practical reason to learn bitwise operation hacks or it is now just something you learn for theory and curiosity?
Bitwise operations are worth studying because they have many applications. It is not their main use to substitute arithmetic operations. Cryptography, computer graphics, hash functions, compression algorithms, and network protocols are just some examples where bitwise operations are extremely useful.
The lines you quoted from the Wikipedia article just tried to give some clues about the speed of bitwise operations. Unfortunately the article fails to provide some good examples of applications.