It depends what your risk appetite is. I see it as layers.

So an organization with skill and motivation, like government agencies vs some specific person with a limited skillset and motivation Who are you trying to "hide" from?

Simply having a different username for each website helps with that. Personally for Facebook / Linkedin I never list my current employer. Enough of a layer to make it harder to track my employer for the casual lookup, but not impossible given enough time/money/competency.

I really like this graphic about what level of security you want vs who you are trying to protect from: https://anonymousplanet.org/media/image3.jpeg