your analogy is off. and the suggestion to use VPN is outright counterproductive.
people close the bathroom door when they poop. I guess they also close the door when they whatch porn.
using a vpn is akin to (car analogy time) trying to using a rental car while in public. you actually expose yourself to the rental company, who might be shadier than the people at the place you're showing up at, who can still see you trhu the window (analogy for your 3rd party cookies)