Do you have to log in to have access to anything on Appian?

You have to authenticate to Appian to have access. This is part of secure-by-design.

What is your use case? What do you want to display to that anonymous user?

Stefan is correct - you must authenticate to access Appian. The only other alternative is to use a service account with a Web API. This allows you to expose information to an integration that makes a request to Appian, and it allows authenticating using an API key that is associated with that service account.

Appian assigns No Access by default to all other users.
Object security is an integral part of application development in Appian, and we should configure the right users and developers have the appropriate permissions within an application and the application itself.

If you want to perform the following activities, then go for Web API. This approach will make your calls easier using key based authentication without having to login manually.

A list of tasks for a specified user
A list of records for a specific record type
Data about a specific record, similar to a record dashboard
An Appian document
The ability to write to a data store
The ability to start a new instance of a process model

For configuring the authentication, follow the instructions mentioned in the link https://docs.appian.com/suite/help/21.1/Web_API_Authentication.html