Sorry, I don't have access to a Mac to test it. Would be nice if someone who can reproduce this problem came to Github and helped diagnose it.

Update: yes, it's a known problem that Brief 2.5 requires permission to set cookies (which also controls database access required by Brief) and thus can't work in private mode or never-save-cookies mode. You may try adding Brief's address (moz-extension://something) to exceptions, but I haven't checked that mode yet.