A VM with a separate OS, talking to the world through a VPN would probably hide you from Facebook, Google, etc, in the sense that it would be hard for them to correlate the two identities.

It of course won't work well against police, who can look up the VPN provider, ask who's paying for it, and it's mostly enough to find you.

They will fingerprint your online presence timing, writing style, forums, audience, etc.

Writing style: this is something you can work on.

Forums: often the need for a separate identity arises from the need to join a particular forum frowned upon by your peers or superiors. Same for audience. That is, if you want a different persona and not a sock puppet to support your "main" persona.

Timing: this is also solvable if you want to.

At some point, following that logic, your multiple online personalities are truly distinct.

For example, "okay, so you have one account exclusively post hard core right-wing arguments in the early morning, and then your second account posts left-wing arguments in the mid-afternoon."

At that point, what's the point? :-)

For many people, the point is posting family photos and cat pics under their real name, for childhood friends and relatives, discussing technical details of some computer game in a slang-rich game forum, and maybe discussing hardcore [insert your favorite bogeyman here] on some forum of like-minded people.

All these three personalities need not be connected in any way, nor need they contradict each other in what they say. They are just for different and unrelated facets of one's life.

You never use multiple personas on a given forum. And you never have multiple public personas using the same language. Routine stuff, such as account management, is OK. Just use the provider's native language.

...and police, intelligence agencies etc... will just flag that and your countermeasures will become a target.