This is really bad. Using a vpn or other kind of service to hide that data from them will now make you even more of an outlier to even more eyes/people. You will stand out from being hidden, you will stand out for having a minimal "internet history", and you will stand out to those who can really fsck your life.
Unfortunately privacy is not being taught and propagated to the general public in order to prevent this from harming you either you want it or not.
Surely the best thing to do is to install software that constantly randomly browses the internet, and properly clogs up any attempt at total logging and/or extracting anything of value out of it. If you're the only one doing it, it will look suspicious, but if you reach any kind of critical mass, I would imagine that it could be quite disruptive.
My plan is to split my network in half, a lot of the traffic I send I really don't care about been monitored (steam/netflix/even work related stuff about programming) but other stuff I do.
That way I'll have a "plane jane" traffic log and some VPN data which is a profile that anyone who works for a large company from home would have.
Unless you put criminal sites in the filter, I can't see how this will help? And if you do...you it will trigger an alert and then they can hax you...legally.
Alternative product idea: An open wifi hotspot that replaces the User-Agent and other client-identifying headers for each session with consistent values, regardless of who is connected. Anybody looking can still see what "your connection" did, but there's no longer any way to prove that any person in your household was the one who made it.
http2 as a transport, some metadata like url or header as a signal for a load-balancer to route the stream somewhere else (to a vpn endpoint in this case).
Unfortunately privacy is not being taught and propagated to the general public in order to prevent this from harming you either you want it or not.