Yes-- same with bluetooth or ordering groceries for delivery and giving your home address. There’s always ways to leak data and make it no longer anonymous. However, from my knowledge of how some of these datasets work, they aren’t putting in a lot of effort into truly trying to make sure the joins are 100% accurate because it rarely matters. They generally don’t give a shit about you as an individual. The most common uses of the data are for advertising and mistargeting doesn’t cost enough to justify the time to verify the data.
Paying in cash though can make it anonymous, or by using virtual cards that mask your card id.
That’s a decent start, but you need a browser that’s resistant to fingerprinting through some plugins and something like ublock origin that will block all embedded content. At some point, it may require you to use a phone number, and at that point you may have a problem. If you avoid that, one of the biggest threats are the facebook and related meta content placed on other pages around the internet. The pixel is one aspect, but almost any facebook content can still track you across sites. These are easily blocked with a decent adblocker and probably privacybadger too.
I know lots of folks will disagree, but I’d care less about Facebook tracking you as they mostly only care about serving you ads and making content suggestions to keep you on the platform to view more ads. Facebook has never served me a relevant ad, and even with a lot of use still can’t recommend things I’m interested in. Data leaks and sharing is a concern, but that’s a concern with every site. I think when it comes to privacy, there’s far bigger concerns.