Your infrastructure will immediately be used to download or upload child pornography. If you're exceptionally unlucky, the FBI will come knocking and, if you're unable to provide them with a useful honeypot, you may risk legal consequences. If you're unable to prove your innocence (the request for the CP did come from your IP address, after all) then you may be very screwed.
I invite the community to toss around ideas about how to protect against this. I hypothesize that it's an unsolvable problem: if you enable strong anonymity, that anonymity will immediately be used for child porn.
One way to combat this would be to have some kind of credentialing, where you are able to generate credentials for the anonymous party to use. Assuming your infrastructure is set up as a Tor hidden service, then it's possible for them to use your infrastructure anonymously, and then you can revoke the credentials for individual violators.
However, under that scheme, your IP address(es) are shared by every user. 4chan will immediately ban all of them as soon as it becomes clear you're a proxy, for example.
It may still be worth exploring, but it needs some thought. Tor itself still doesn't have "endpoint bridges," that is, endpoints which aren't publicly listed. Meaning it's very easy to ban all of Tor, as far as I know.