There is too much demand for this to exist for more than a blink of the eye. Any public proxy you find will either cost money, exploit your traffic to make money, or be too overloaded to be reliable.
However, some cafes and public libraries offer anonymous wifi, so if you don’t use a lot of bandwidth, they might be worth trying.
There is also Tor.
nginx is free and reliable, I’ve set it up for http, tcp, and udp proxies
What you need to do? Would a VPN work for you too?
You don’t use HTTP or SOCKS proxies to proxy internet traffic these days but VPNs. The effect is the same but it’s a shiny new name to market. If you’re talking to a normie (i.e. Google), you’re looking for “a VPN”.
This space is quite crowded as it’s a super simple service to offer and is insanely profitable. You’re basically being resold datacenter bandwidth with a profit margin of at least 90%.
What you’re likely looking for (given the community) is a proxy to pseudonymise your internet traffic such that neither data brokers nor governments can trivially get access to this information.
Given the insane profit margin, there are tonnes of unscrupulous “VPN services” that stab you in the back and double dip; selling your traffic data to the highest bidder. If you want one who doesn’t do that, you must pay and even then you have to be extremely careful in your selection. Unless proven otherwise or very implausible, assume any VPN proxy provider stabs you in the back for even higher profits.
The only exception I know of is ProtonVPN which offers limited free servers. The free tier is effectively a free trial with some limitations, namely that it’s only a handful of countries and that P2P is blocked. I’ve used it for years and IME speed has almost always been absolutely fine.
Whether you trust Proton is up to you to decide. IMV the company does not appear to be in this primarily for enrichment but because they actually care about privacy. They offer quite a wide range of other services that they built from the ground up and largely open sourced. The raison d’être for their free VPN proxies appears to be customer aquisition and I guess it worked on me because I’m now a paying customer of theirs, though primarily for their email services.
Note that they comply with (Swiss) government orders (as any sustainable business must) but I trust them to not sell my data to the highest bidder or governments which is what I care about. If you’re doing shit bad enough that could get someone to convince the Swiss government to go after you, they will not shield you (but also just… please don’t).
You could self host one
Conceptually, if the thought is to hide traffic, self hosting doesn’t add anything, unless you make it public (which I wouldn’t) and have multiple people using it.
I think in this case “self host” would be on a VPS, not at home. But you definitely would want to lock it down so it was open to the public.
If it’s on a VPS, the host can see your traffic. That may or may not be an issue for you.
Squid? Nginx? Not sure I understand the full scope of the question though
if you want to hide your IP or location then use TOR
Privoxy maybe
