Yes, there are hosts that can be paid anonymously in cryptocurrency. Here's an updated version of my list of suggested hosts and registrars:
Potential hosts I know of for a (/v/-only or just a few boards) webring site, does anyone have others to suggest? I am not an expert and mainly went by hosts I saw others using or recommending as free-speech hosts, this is not exhaustive.
1. Buyvm.net, which used to host Fatchan and still hosts Julay and smug. Obvously the fact they took down Fatchan is not promising, but supposedly part of that is because they were using anycast IPs that relied on Voxility. Also the log mentions Fatchan's (almost entirely inactive) /pol/ board so a /v/-only board might not run into that problem.
2. www.trabia.com, the host in Moldova used by Exhentai. Not sure what their stance on "hate speech" is but for a /v/-only site they might be good, hopefully a loli-allowing host in Moldova isn't going to flip out because someone in a videogame thread said "nigger". Their TOS mentions they will ban you for certain illegal activities but doesn't mention any non-illegal things they will ban you for. Has their own DDOS-protection service included, though it looks like if you actually come under attack and need to announce prefixes they charge you 100€ per month, probably more than you'll be paying for the hosting itself.
3. Steadfast.net hosts Sankaku Complex, including their booru that has a loli tag and makes no attempt to hide it. They are probably the most mainstream host on the list and seem to cater to businesses. Requires you get a quote from them rather than having prices on their website. In trying to look up their policies I saw this 2014 Slashdot comment:
>SomethingAwful is over at Steadfast.net, who has a rather first-amendment heavy interpretation of most laws. I know first-hand how their abuse desk works, and they'll allow practically anything that's not explicitly illegal.
While obvously allowing SA is not the most glowing recommendation it might indicate they don't respond to frivolous complaints, since SA used to piss plenty of people off back in the day. Their TOS doesn't allow piracy even via hosting torrent files rather than content itself. Unclear how they would handle either /pol/ or offensive content on non-/pol/ boards.
3. nearlyfreespeech.net Included because they're a U.S. host named after free speech that supposedly takes it seriously, but it looks like their pay-as-you-go pricing scheme might be too expensive for an imageboard.
4. zensurfrei.com I don't know anyone that used them but their entire website is about how much they care about free-speech and how they don't believe in hate-speech. Might be more oriented towards /pol/ but they probably allow loli too. Their site is pretty ambiguous about exactly what sort of resources they give you for any particular price, you have to talk to them. I read a comment that you pay them by mailing an envelope of cash so it might take time to set up.
5. Flokinet talks about free speech on their website but here is someone talking about how they banned his site for offensive content:
6. 1984hosting.com Based in Iceland. Named after the novel and in the same Slashdot thread someone said "they have defended their customers freedom of speech all the way up to the highest court in Iceland numerous times", don't know how true that is nowadays. [UPDATE: I have been informed Iceland explicitly bans loli and has have-speech laws.]
7. alexhost.com Another host in Moldova, they proudly boast about ignoring DMCA (which they can do since they're not in the U.S.), but the page also mentions freedom of speech and only mentions illegal activities as banned.
8. ititch.com U.S. host, their website proudly talks about how they're committed to free-speech and privacy and will keep sites up in the face of opposition. Primarily (only?) payable in bitcoin, and lets you pay anonymously. However their low-priced options all have a pretty small amount of storage space, so for an imageboard it might be too expensive. I'm not sure just how much storage space would realistically be needed.
9. lolekhosted.net Moldova host, their website proudly brags "Never Receive Abuse Complaint", "You can host anything here!", "Marketing Emails, Scanning and more allowed", and "no-log policy". Clearly they cater more to piracy, spammers, and criminals of various sorts. But presumably at the point where you put "Never Receive Abuse Complaint" on your website you're not shutting anyone down for loli or controversial politics either. Can be paid in cryptocurrency. Be careful about backups in case they suddenly get shut down by Moldova police for some of the other stuff I assume is on their servers. Supposedly they've been around for 11 years but it looks like they were in Poland instead 2 years ago (according to a comment that said they allowed anything except CP). Only offers 40GB of space unless you're paying $100 per month or more, so same potential problem as the last one.
10. Colocation. I don't know much about this but colocation services might be more permissive. I noticed Trabia offered it but there are countless others.
11. Having a server in your house and paying for some sort of business account from you ISP that gives sufficient upload and doesn't forbid servers. Shows your IP if you don't use a service like Vanwatech or Cloudflare. Hard to shut down if you aren't doing anything illegal in your country, because it's your own damn server. If you compare with the plans we're thinking about it's not like the nessesary hardware is really all that expensive, and some or all of it might be in a spare computer you already own. The business account is probably the more expensive part, depending on where you live.
1. Eranet International at Now.top is some Chinese (formerly Hong Kong) registrar that hasn't taken down 8kun.top despite extensive efforts against them, after several other domains were taken down. That seems as resilient as it gets.
2. Smug just switched to Tucows. They banned 8chan but should be more resilient than most to a random angry email. It's looks like Tucows doesn't sell them directly but goes through various resellers, so you would go to a Tucows reseller like EasyDNS, which supposedly is resistant as well.
3. r01.ru is used by dailystormer.su. They used to be at dailystormer.name using Eranet, and that domain is still under Eranet and redirects, so they weren't taken down from there either. Russia bans loli, I don't know if that would affect the decisions of a registrar. Looks like their website is only in Russian, which might be inconvenient. Searching their name finds this wiki complaining about them providing services for fake pharmacies, and they have a list of other offenders that might be of interest:
Obvously just because a registrar allows criminals doesn't mean they allow legal but controversial sites, but it might indicate a registrar that just doesn't care about complaints in general. (For example I saw the aforementioned EasyDNS praised on blackhatforums for "only suspending sites for a court order", but they're a reseller for Tucows which banned 8chan. Though as mentioned they still might be better than most for sites that don't attract 8chan levels of notoriety.)
4. On a similar note here is an article with a list of "bulletproof" registrars used for piracy sites and various illegal activity. https://web.archive.org/web/20200430160454/https://email@example.com/bulletproof-domain-registrars-in-the-world-c749d5e66259
However note most (all) of them are resellers rather than ICANN accredited registrars, so someone could go further up the chain to see if the company they resell from will ban you. But some of those companies they resell from are Chinese or whatever and probably don't care.
5. Some of the registrars on this list of hosts and registrars that allow warez might be okay:
Many of the hosts aren't, I went through the lists under "U.S.", "Moldova", and "Other Hoster with many locations" and incorporated a few good ones but the others had policies against "racial hatred" or the like. Registrars seem a bit harder to evaluate but the nice thing with them is they just need to send it out to DNS providers, there's not really technical requirements and weird foreign registrars should work just as well.
Technical requirements and pricing
The Fatchan board owner said he paid around $50 a month and didn't hit any limits hosting all of /v/. The Julay/meta/ sticky says this about their server:
>2x Intel(R) Xeon(R) CPU E3-1241 v3 @ 3.50GHz 8GB RAM 180GB SSD
DDOS-protection, if it ends up being nessesary, is trickier and ranges widely in price, from free to significantly more expensive than hosting, and different types of DDOS protection might not be very similar.
Also the owner of anon.cafe recently uploaded this which might help make it easier if someone wants to try making a Fatchan sucessor (though it's for Lynxchan instead of JSChan if you want the same software as well):
InstantIB.LynxChan: An Imageboard Host Builder