Can I export my funds from blockchain.info with the backup phrase? For some reason lately Blockchain.info's 2FA emails haven't come through. I tried resetting 2FA emails with my back-up keys and did it successfully but now the 2FA emails aren't coming to the new email. So something is totally off on their side. Is there a way I can export my funds (BTC/ETH) out from blockchain.info without knowing the private keys for my addresses but only the back-up phrase?

Thanks!
If you mean by "backup phrase" the Mnemonic phrase which is 12 word for blockchain so the answer is yes, you can export your funds.

Assume you want to import your mnemonic phrase to electrm

you have to choose that your mnemonic phrase is bip39 seed, not electrum seed. 

Then they will ask about derivation path you leave it 44 (default) for blockchain.