Private browser mode in many browsers disables plugins by default, and also doesn't do anything to stop trackers or data collection. All private mode does is keep your activity private from others who also have access to your device (e.g. family members, roommates), by not saving browser history/cookies/etc.

Also, VPN's can be helpful, but there are ways to "fingerprint" individual users behind VPN's by how they move their mouse and click speed and what websites they visit etc… I imagine plugins like AdNauseum could help with that. It's a clever idea, I'll have to check it out - thanks!