Comment by BolexNOLA
I’m not sure who “the market” is in this case, but reCAPTCHA is owned and implemented by Google and clearly favors their browser. Any attempts to use other browsers or obfuscate your digital footprint in the slightest leads to all kinds of headaches. It’s a very convenient side effect of their “anti-bot” efforts that they have every incentive to steer in to.
This isn't Google's doing but Mozilla's. Firefox's strict tracking protection blocks third-party cookies. The site you're trying to visit isn't hosting reCAPTCHA itself; reCAPTCHA was loaded from a third-party origin (Google); so the cookie that Google sets saying you passed the CAPTCHA is blocked by Firefox.
You can add an exception in Firefox's settings to allow third-party cookies for CAPTCHAs. Google's reCAPTCHA cookie is set by "recaptcha.net", and CloudFlare's CAPTCHA has exactly the same problem, whose domain is "challenges.cloudflare.com".
If the cookies aren't set and passed back, then they can't know that you've solved it, so you get another one.