Are there any exchanges that don't require photo ID, or other personal info, if no fiat currency is involved?
Only crypto in and out.
Heaps of them. I'd say basically any except for bittrex or poloniex but obviously rules will differ from one exchange to another, and also you should consider the fact that how much you trade has got a lot to do with whether or not you're going to pick a particular exchange as well.
Though, these exchanges who do not need an ID generally are from unknown origins, meaning that storing large amounts of funds is discouraged.
Are there any exchanges that don't require photo ID, or other personal info, if no fiat currency is involved?
Only crypto in and out.
Try coinomi.com. AFAIK it doesn't require an ID to trade cryptocurrency pairs. Yobit also doesn't seem to require an ID. I have traded and was able to withdraw without giving any personal details.
I heard that Bittrex started to ask people to verify but I still have an account there which I can use in full and they haven't asked me for ID at all. Maybe it's only for new users.
Coinomi is a wallet, not an exchange. They use changelly for in-app exchanges.