Protonmail goal is to preserve privacy, while Google's goal is to collect your private data.
Please be more concrete. What exactly is the risk here? That Google can look into the logs and infer a Mac OS Bigsur with Chrome v90 is logging into proton mail today at x:xx pm?
Google is discovering that this particular user is ripe for advertising security related products.
So the ultimate risk of using ReCAPTCHA on proton mail is that Google might find out I'm more tech savvy than the average? Fine by me.
Those are your values. Other people have values that they don't want to be tracked and profiles made on them as they move around on the internet.
No, no. Now Google knows you are using ProtonMail, and by extension the NSA knows you are protonmail, the FBI knows you are using ProtonMail, and so on.
This may or may not be a problem for you.
meh, if FBI is truly trying to track you down, they have an easier time accessing your ISP and mobile carrier logs to see what IPs you've been talking to.
Maybe yes, maybe no. The more information you leak the more opportunities to find easier ways.
Less likely to do that if you're not appearing in a "people who use protonmail" list.
Google has history of this user logging to protonmail including ip adresses. Google gives that log to US agency, US agency correlates that log with the log coming from ISP and identifies the user.
They can correlate your login timestamps with emails you send to gmail users and identify your protonmail account.
It goes against the very reason of Protonmail existing. If you are to accept privacy leaks by design, you have no reason to use what Protonmail claims to offer in the first place, and just stick with gmail.