In cases like these, I use multiple personas in Chrome (I think Firefox has user profiles) so I can log into my personal accounts on my work computer while still keeping everything compartmentalized.
I'm glad that works for you, but I follow a strict policy of separation between work and personal accounts and technology in order to support a defense of my open source work against any claims from current/past employers regarding IP assignment. I have a completely physically separated space, network, and internet connection specifically for work usage and there is no account or physical crossover between work and personal computing. I /never/ login to personal accounts from a work device, and I never will, browser personas is not a sufficient protection.