BlueMail connects to virtually every email service, anything offering standard IMAP and SMTP, plus OAuth sign-in for Gmail, Outlook, Yahoo, iCloud and the rest. Proton Mail is the rare exception, because it deliberately keeps third-party apps out of its mailboxes.
So a @proton.me or @protonmail.com address is one to keep in Proton's own app, and the good news is you can stop hunting: this is a Proton design decision rather than a setting you have missed, on every platform.
Why Proton works differently
Proton's privacy model keeps your mail encrypted in a way that standard IMAP and SMTP cannot carry, so instead of opening those protocols it routes third-party apps through Proton Mail Bridge, a separate desktop program, and states in its own documentation that "we do not offer POP3 support".
Bridge is a desktop-only program, so it is not a route a mobile mail app can take, which is why Proton mailboxes stay in Proton's own apps.
The setup that works well
Use Proton's own app or webmail for your Proton mailbox, and keep everything else together in BlueMail, Gmail, Outlook, iCloud, Yahoo and any standard IMAP or POP3 mailbox all work here, with a Unified Inbox across the lot. See Which Email Providers do you Support? for the full list.
If a Proton address used to work in BlueMail, this is the reason it stopped, so you can save yourself the troubleshooting. To tidy the old entry out of the app, see How to Remove and Re-add an Account.
Adding a different account
Adding any other mailbox works normally: enter your email address and password and let BlueMail detect the settings. If a different provider is refusing to add, see Why Won't My Account Add? Quick Fixes for the one thing to change, or Can't Add My Account for the full checklist.
