Replacement Login

Blogger
For 2FA, many people give over their phone numbers and device information, and additional information to Google to protect their data, but all of this metadata is then linked with your Google account.

Replacements
There are several other 2FA services available which do not require sharing more data with Google, but they have widely varying privacy policies.

Authy https://authy.com/ Authy is a 2FA service owned by Twilio. It offers multi-device and cross-platform support. While their privacy policy is far from perfect, they do not sell you data to marketers.

andOTP https://github.com/andOTP/andOTP andOTP is a free and open-source 2FA program for Android only. If you only need to use 2FA via an Android device, this app is a great option.

LastPass https://lastpass.com/auth/ LastPass Authenticator is a a 2FA service from LogMeIn. It offers extensive features, including one-tap login to many top sites. However, it only works on mobile, and tracks users' location and device info, and they purchase third-party data and combine this with your app data.

BitWarden https://bitwarden.com/ BitWarden is a cross-platform, 100% open-source 2FA service. Most importantly, it allows for self-hosting, and the company states plainly that they collect minimal data and do not sell it to third-parties.

Duo http://duo.com/ Duo is perhaps the worst option for 2FA from a privacy standpoint. It is owned by Cisco, and they not only collect data from you and your device extensively, they both buy and share your data to combine it for marketing purposes.