As a newsletter company, we've dealt with this for over a decade now since we do the right thing and do double opt-in which involves sending the subscriber an email on signup.

Until a few years ago, IP reputation was a good defence against this. The bad traffic almost entirely came from IP addresses in certain countries or from datacenter IPs we could block. Nowadays, that doesn't work due to the prevalence of VPNs, so many legitimate users appear to come from low reputation IPs.

Turnstile is a reasonable solution in its normal form, though the 'invisible' option still lets a lot of them through. Another thing that works, surprisingly, is looking for "webdriver" usage. Despite being easy to strip out webdriver fingerprints, we find that the majority of automated attempts do not bother to do this. Adding more steps, honeypots (with an immediate short term IP ban), etc. also have an impact. It becomes a game of piling up numerous defences in a sort of "Swiss cheese model".