Do you really need the Tor browser to do this?

I just sign into Facebook, Google, &c services using one browser, and do everything else in another — all of which all have µBlock Origin, Privacy Badger, whitelist-based cookie managers and the like installed.

EDIT: One advantage of this approach is potentially significantly raising the noise floor in Tor traffic. That, by itself, is a win.

EDIT 2: Also IP-level tracking and fingerprinting. See below...

Do they not try to match you based on your IP?

After all if they know it is a residential IP, they probably know that no matter the user-agent, traffic belongs to the family. And I assume they know who all your family members are.

When you use tor it says not to maximize the window because sites can use your screen resolution to track you. More realisticly they could match operating system from the user agent with other data. I remember chrome being acused of putting serial number like strings in the user agent. Why would they not?

These are the basic basics for tweaking FF's about:config. There are many more. Try these and see how you fare...

layout.css.visited_links_enabled set to false; geo.enabled set to false; media.navigator.enabled set to false; media.peerconnection.enabled (WebRTC) set to false; network.http.sendRefererHeader set to 0; privacy.resistFingerprinting set to true; privacy.firstparty.isolate set to true; network.dns.disablePrefetch set to true; network.prefetch-next set to false; webgl.disabled set to true

Don't forget to also use something like uBlock Origin, Token Tracker Stipper, and Decentraleyes. Pass is all through a Pi-hole and VPN and you're pretty safe. Make sure your VPN does not expose your NAT'd IP with WebRTC. Both uBlock Origina and ScriptSafe can help with this, as FF will sometimes crap all over its about:config settings with updates.