There are about five hundred services that need to do this, to be honest. The separation between a user and an account is one that's largely not valued when people are originally modeling applications, but it probably should be. (Speaking for myself as well here.)

The way I work around this is launching a separate chrome for each account.

For example, I have a work-trello and a personal-trello command in ~/bin, but you can use shortcuts in Windows or whatever the equivalent is in OS X.

chromium-browser --app=https://trello.com --user-data-dir=/home/jewel/.profiles/personal-trello

They can run concurrently and are completely isolated. I don't think this is possible with firefox yet. I use app mode since I don't need the normal navigation when using it this way.

Firefox has done this for a very long time: its called profiles and you can read up on it at https://support.mozilla.org/en-US/kb/profiles-where-firefox-.... You can simply run

firefox.exe -p

and pull up the profile manager (you have to make sure all instances of Firefox are closed first) and you can create as many profiles as you want. Once you have a profile (for example, "worktrello") you can launch it with

firefox -P "worktrello" -no-remote

and it will be a completely separate process, with its own cache and cookies and all.

Same with Chrome, only it has a UI. Click the person icon at the top left.

I know you probably don't want to move, but slack.com has done multi-account management for team chat really well.

trello needs to do this.

Yeah, for Trello, I have to switch Google accounts to go between personal and work boards. Kind of a pain.

seriously