Neither Set List Maker nor BandHelper require a login to open the app. This is partly for convenience and partly because your data is stored locally for offline access. If the apps supported logging in and out with different usernames, then either the apps would need an Internet connection to see different users' data (not practical at most gigs) or they would need to download and store all users' data just in case it would be needed (extra effort for a limited use case). Essentially, iOS and Android devices are single-user devices and my apps fit into that paradigm. If the devices ever gained multi-user capability at the OS level, then my apps would automatically gain that same capability.
If you want to let someone use Set List Maker on your device, but not edit anything, you can go to Settings > Database Sync and turn on Read Only, then turn it off when they're done. If they wanted to, they could go turn that off themselves, but I assume your bandmates don't have malicious intent when accessing your band's data and you're just worried about someone making a mistake. Of course, you can always roll back any changes, too.
In BandHelper, user privileges are set by administrators from the web interface. So to do this same trick in BandHelper, you'd have to log into the web interface and change your own user account to Read Only (but leave it as an administrator, so you can go back and turn that off later). Since BandHelper supports different permissions for each user, and these permissions are only available to administrators in the web interface, users can't go into the app settings and change their own permissions.
In case someone is tempted to change the username that you are logged into in BandHelper, I'm pretty sure that would cause problems. The username is editable so you can change your username (you'd have to ask an administrator of your account to change it in the web interface first), not so you can log in as a different user. If you needed to change the user identity on your device (e.g., you sell your device to a bandmate) you would remove the existing account from the app, then add a new account under the new username. But that re-downloads all the data, so it's not something you would just be able to switch back and forth with.
I hope that helps...