Like I read into this and found that e621 if your account gets banned then any account in that same household gets banned, meaning this website won't consider facts like different person in a household. It does seem kind of strange because I have login through other households before, and imagine being in something like a hotel what then? And what if you move and then the next person has a e621 account? I guess there can be considerations, as I do think getting a different internet provider or router does change IP.

It isn't considered because the excuse is too convinent and next to impossible to prove without basically doxxing yourself

Adding on to this, there really are not that many bans/records, the site has ~27.2k active (~30k total) bans and 72.6k records

There are 4.3 billion (2³²) ipv4 addresses in the world, and 340 undecillion (2¹²⁸) ipv6 addresses

Even if you significantly reduce ipv4 down to 100 million to account for business usage, private networks, and a ton of other things that is still an immense amount of possible ip addresses, the chance of overlap are astronomically small (using 100k as the total and assuming every ban/record has a unique associated ip, that's a 0.1% chance)

Now, if you live in a particularly furry place then those chances would be higher, but still likely negligible

ip matches also are not instant bans, the staff look for matching behaviors and other things

I knew of this one user from 10 years ago that used this very excuse in a bid to avoid getting permabanned alongside his alleged housemates.
I recall him using the excuse somewhere along the lines of "we all used the same wifi in the house", and if he had made a rule-breaking comment, "we also used the same PC and my roommate logged into my account instead" and then going on an argument between the accounts of their housemates (which would look like the same person replying to themselves on an alt account).
Needless to say, all accounts under that IP got blanket-permabanned for being alt accounts. You can see why same household accounts would be a mess to moderate.

I'm pretty sure if you were travelling out of home and then logging into a massively shared wifi spot (such as university wifi or such), you won't get banned for being in the same IP as a previous user whom had been banned there before.
The admins probably have a way to keep track of your IP addresses which you logged in from and see if you are in any way related to the permabanned user.
In most cases, it would also require someone to report your account for ban evading for you to be placed under scrutiny as well.

thegreatwolfgang said:
The admins probably have a way to keep track of your IP addresses which you logged in from and see if you are in any way related to the permabanned user.

Without getting too much into the weeds, admins can see all ip addresses a user has done some actions with, it's rather limited (only tracks the most recent login and a few common actions like creating comments, editing posts, etc) and not all that useful unless there is already suspicion, as you alluded to:

thegreatwolfgang said:
In most cases, it would also require someone to report your account for ban evading for you to be placed under scrutiny as well.

This is becoming a larger problem now IPv4 addresses are being exhausted and many ISPs (especially phone carriers) are resorting to stuff like CGNAT, but e621 is probably still small enough that it's not a problem. When I lived rurally in the USA we only had one ISP available for miles, I'm not sure how big the IP pool was (they were subleasing from a larger ISP so they likely didn't have access to the full range) but everybody I knew locally had the exact same IPv4 address, so there were probably hundreds if not thousands sharing a single address.

Every few months while reading Wikipedia I'd get a giant banner at the top of the page telling me I'm banned because somebody sharing the IP address vandalised an article, but I still doubt many of these people would have an e621 account. And if they did, they would most likely be part of the 98.63% of registered users that are not banned.

It's also worth noting that staff are likely just not going to be bothered to track down every account and try to eradicate a banned user out of existence. It's not like they have an alarm that goes off whenever a banned user tries to sign up again, unless a user is exhibiting the same bad behaviour it's unlikely anybody is even going to go out of their way to check.