If a website offers you to sign-in using Google (or any third-party service, say Facebook, Github, etc.), don’t use that feature.
The long and short of it is that if Google (or third-party of your choice) locks your account for some reason, you will be locked out of all the services where you signed into using Google. There’s no shortage of examples where people have been locked out of Google (and other services), with no recourse to re-enable their accounts, and consequently losing all data hosted or protected by that Google account.
Every respectable service allows you to create accounts using your email address, so please use that method to create your accounts.