We understand that there may be times for certain users that MetaMask doesn't meet their needs - whether it be from a token management perspective or otherwise. This is why we have built our product on open standards, allowing for easy cross-platform usage.
MetaMask uses a 12-word seed phrase to manage keys and accounts for users. Instead of users needing to backup JSON file data or private keys, we allow multiple ETH addresses and corresponding tokens to be managed and backed up simply through the one 12-word seed phrase.
To use the Ether addresses associated with your MetaMask account on another site or tool such as My Ether Wallet, Parity, Jaxx, ImToken, etc you can use the 12-word seed phrase to pull up all of your associated accounts and select which one you'd like to use.
Alternately, you can export your private key from MetaMask and use that individual private key to access a single Ether address.