I suspect a lot of it comes down to your ISP. Like the original commentor I also frequently can't pass CloudFlare turnstile when on Wifi, although refreshing the page a few times usually gets me through. Worst case on my phone's hotspot I can much more consistently pass. It's super annoying and combined with their recent DNS outage has totally ruined any respect I had for CloudFlare.
Interesting video on the subject: https://youtu.be/SasXJwyKkMI
There's no alternative that won't have major limitations. I predict it'll just be more like going back to the days of jailbreaking to install unsigned apps. Unfortunately AOSP is already pretty much unusable without Google services installed for the vast majority of apps.