Why not whitelist the cookies of sites where you're going to log right back in?

That's actually a good idea! It doesn't work for Google or Facebook tough, or other services I explicitely don't log right back in.

Firefox Containers work great for this!

I second Firefox Containers.. very useful feature.

I guess this isn't typically based on cookies but device/browser fingerprinting.

Which is exactly what I'm trying to avoid. I don't want to be tracked so I try to limit the amount of fingerprinting possible.

But for this it is probably good that the services do fingerprint us - so that we understand how well it can work. Otherwise we'd assume that cleaning cookies is enough and wouldn't know how well that tracking works, not only when services that we knowingly use are doing it, but also when some actual black hats do it.