If you do move on, please take a minute to contact the Website or service and tell them why. If "we" just collectively walk out they might not understand why.

In order to make this easier I wrote a short template :

To whom it may concern, I tried visiting your Website today to use your service as it looked like what I need. Unfortunately the verification method you use requires a mobile phone verified by Google. This is not something I have nor do I want to due to privacy concern. Google being a large and powerful advertising company I do not trust them with my data. Do you have an alternative way for me to confirm that I am indeed not a bot that puts your service at risk?

Feel free to use this verbatim or adapt it and share back.