Can a CSPRNG, seeded with a key, be used to generate a byte sequence as long as the plaintext to XOR it with that? Given a “safe” (meaning: brute-force is your only shot) cryptographically strong PRNG, wouldn't it be safe to encrypt data using the CSPRNG to create a key as long as the data and then encrypt the data by XORing it with the key?
Yes it would.  

As CodesinChaos reminded us in his comment:


  We call that a (synchronous) stream cipher.


Look up RC4 and A5/1, two of the most statistically popular ciphers in the universe.  Also compare to a correctly generated one time pad.  Not a lot else to say at this point.