How can one disable, or at least tone down, the gore in Bioshock Infinite?
No I'm afraid you can't. There is no such option in any of the menus, not even in the PC version. I searched around a bit, but for this game this isn't an option.
Also, if you read some articles you'll understand why. Just a small excerpt:
The thing is — and this is possibly a spoiler — you’ll use your face-ripping, flesh-melting, eye-pecking weapons and powers to take out white supremacists. That’s game violence put to good use.
I am pretty sure that you can't tone down or disable the gore/violence. At least on consoles.