Why do people have it in their head that their IP address being known is basically the same as having your pc connected to public wifi while running windows 98?
Your ip address isnt really private and if you want to keep it hidden use a vpn, problem solved.
Because it used to be the case that everyone connecting to the Internet had their own personal IP address, and service providers would route almost all packets for it straight to your network interface, no questions asked, with all the entailed security implications. It's true that today's niggercattle have little to fear from their NAT's IP address being visible to some webmaster.
The answer is:
Depends.
A very big depends, hence the emphasis.
Ever since the IPv4 pool got exhausted, every RIR has been juggling IPv4 addresses via NAT, diluting them more and more just to ensure everyone is still connected to the Internet. Nowadays, in practice, it means that your public facing IP fits one of these three criteria:
a. Static IP
b. Dynamic IP
c. CGNAT IP
In the first two cases, the endpoint between the Internet and your local network is your router. This means that when someone gets your IP, they get a pointer to your router from the Internet, and your router is now the only thing stopping hordes of port scanners from all over the world finding an exploit and breaking into your network to then commit wire fraud or other nefarious crimes from your connection so that all the blame lands on you and not them. In case of a static IP, your IP is a permanent link back to your network. In case of a dynamic IP, a router restart (more specifically a PPPoE/DHCP session reinitialization) or simply passage of time will roll a new IP for you, and the old IP will now point to a different client.
Now, in the last case, what happens is that your IP is shared with other clients of your ISP. This is what's known as CGNAT, or carrier-grade NAT. In this case, the endpoint is your ISP's datacenter, so if someone obtains your IP, they can't do jackshit with it. These are becoming more and more common, but classic IP assignments that point to your router are still prevalent. If you can open a port to torrent or host a game server, you have a classic connection where your router is the only thing between your network and the hostile environment that is the Internet. If you have an insecure router, that can fuck you over. If you opened remote management ports, or other ports, like for torrenting or hosting game servers, without understanding what it does like an idiot, you know damn well that every possible exploit under the sun is gonna be tested on those as soon someone sniffs them out.
Going back to the initial question, why do people still fear that someone getting their IP means they're fucked? Simple, they heard some valid anecdotes about public IP addresses, but they have no understanding of their home network so they make irrational assumptions out of their own lack of knowledge. CGNATed connection? Nothing to worry about. Fancy prosumer/enterprise router? Hopefully the guy that installed it for himself knows what he's doing, and if he does, he knows he has nothing to worry about. A static/dynamic IP on a chinkshit ISP router or an old TP-Link? A disaster waiting to happen, possibly already a part of a DDoS botnet. Which one does the normie have? He has no idea, he's too tech illiterate to verify, so he will panic. Jason sure as hell wouldn't know what I'm talking about, but he sure would parrot it all with confidence like he knows shit.