The limit between full anonymity and pseudo-anonymity is not that clear. One normally call pseudo-anonymity the state where it is still possible to know who was responsible for what.
And a site developper can not guarantee that his site enforces fully anonymity, unless he is at the same time the site administrator. Because even if the database does not keep IP addresses, and only keep hashes of the email addresses, underlying systems such as various proxys or reverse proxys could generate logs containing the IP source address, the time of the request, and the type or size of the request. On a not too busy site, that is enough to find the originating IP for any message. Other logs could also exists independently of the database. For example some authenticating libraries could log each successful login with the login name (normally a password is never willingly logged) and enough information (still the time...) to successfully link it with the IP source address of the request.
What I mean is that only a deep inspection of all logs existing on the platform hosting a site can guarantee the anonymity of the site. And I would not be very confident here, because security best practices require that logs are generated and kept enough time to be able to discover and analyse a possible attack, and those logs could be stolen or given to the authorities in case of a legal enquiry.
So the more you can do here is to claim that you do your best to preserve anonymity and never store, use or sell personnal data, and if possible show external audits proving it.