I understand it's difficult to do, but if you're a service that encourages it's use across work and personal life, you eventually need a way to manage people separating that.

Perhaps they can have the concept of you always have a personal account, and you get /invited/ into an organisation? As apposed to Google's approach of having seperate, distinct accounts and you can 'easily' switch between them.

That sucks, and causes problems. Dropbox tried it. On the organisation side, they now have to remember that user redpuppy925 is actually an org member, rather than by the organisation identity. Then the user interface would have to show their personal and org content at the same time. You really don't want that happening on their home family computer, nor would the user likely appreciate their personal content always being available at work. It ends up far easier putting the wrong items in the wrong place.

As an org admin, it should be very clear who has access to org information. And when they leave it should be very easy to revoke that access. Backups and auditing should only cover org data, not personal content.

- use different browsers (Chrome, Firefox, Opera).

- or use different users (feature introduced in Android 5.0).

Less than ideal (e.g. opening link) but can be useful sometimes.

On iPhone maybe iOS Chrome and Safari Mobile have different cookies so can have different users?