[nitrogen]

I wish Firefox provided two intents (does Android still call it that?), one for normal browsing and one for private browsing. Then any app that opens a link doesn't automatically get your active cookies from your main browser if you don't want it to.

[smichel17]

Settings > Private browsing (under Privacy and security) > Open links in a private tab

An alternative is to use Firefox Focus (Firefox Klar on F-Droid) as your default browser, then its "open in" feature if you want to make it a permanent session.

[Osiris]

I use Firefox Focus as my default. It does this. No tabs, no cookies.