I'm not saying the browser isn't a
factor, or that Google isn't anti-consumer, or anything else. The original comment didn't say they were caught up in some unobservable AI machination. They made a pretty straightforward observation mentioning only two conditions: Google bounces them when using Firefox. From that, they jumped to a pretty straightforward conclusion— Google transparently harasses Firefox users to advance their corporate strategy.
I'm not going to jump through hoops to prove a negative, but correlation does not imply causation.
My empirical observation: For many years I have constantly used Google search on FF with many machines and networks, logged in and not, in private mode and not, with all existing privacy features enabled and no extensions beyond a password manager. Napkin math conservatively estimates I've conducted 200k searches minimum using this combo. I've consistently encountered suspicious activity challenges when using overcrowded proxies, NAT'd networks and VPNs. Removing those factors has never failed to stop the challenges. Ever.
I'm confident the poster's observations are accurate. My observation does not directly contradicts their observation, but it does contradicts their conclusion.
I wouldn't be surprised if other factors like JS being enabled, cookie settings, plugins that affected those things, number of other users on their network, or even the public IP range they fall under would affect it.