Presumably the like button wouldn’t work - but that’s what I want. So the Q is: what will break that I didn’t want to break?
It can. Blocking third-party cookies is available in the browser settings of at least Firefox, Chrome, and Safari. I think it’s even on by default in the latter.
I’ve been using it for years and never seen a broken page as a result.
Sites that put a checkout flow hosted on a different hostname in a subframe break.
Some forms of "sign in with X" break.
But there's a thing for Firefox which does it for all sites. Called First Party Isolation.
Obviously this would need a white-list (and a pair<from,to> whitelist, not just "this domain is OK list) to allow SSO scenarios.
This will treat every first party domain as it's own container for cookies and other stuff.
This extension gives Firefox selective amnesia: if you're in a Facebook container tab, it'll remember and send those cookies. If you're not, it won't!
An alternative solution is to never make those third party requests in the first place, but you might need some of them for content you're actually interested in viewing. Using both a blocking extension and this container extension should improve your privacy towards Facebook.