I'm not sure what exactly the hosts you're referring to mean by "anonymous", but to me it usually means that the WHOIS details of the IP addresses and hostname are anonymized so nobody finds out who you're hosted with. Useful for resellers.
I'm sure that there's no company which doesn't require at least your name and address, but I can very well imagine that you'd be allowed to host your content on servers located in countries where fights are legal. As long as you're not involved in those fights, I don't think there's much the police could do against you. You'd only have to make sure that everything is on the server and not on your computer, just in case they find out about you and decide to examine your computer.
I'd definitely ask a lawyer what would be the best way to host that kind of site so you won't get in (too much) trouble.
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