Google Classroom is no longer restricted to users on the same domain. If you have an @gmail.com email address you can go to http://classroom.google.com and create a class. You can also join a Google Classroom class by using your personal Gmail account.
For Everyone But…
This does not mean that you can use your personal Gmail to join anyone’s Google Classroom. You can if the teacher made the class in Gmail but not necessarily if it was created on a school domain. School accounts are managed by the G Suite admin. In order to join a school Google Classroom class the G Suite admin will have to have checked some checkboxes in the admin panel to allow it. This is highly unlikely to happen at most schools.
G Suite Admin
If your G Suite admin is willing to allow personal Gmail users to join the domain they will need to go to http://admin.google.com and under Apps, choose G Suite, and then expand the settings for Google Classroom. They will want to choose “Any user” for both who can join classes and for classes you can join.
Go Slow Workshop
Alice Keeler has Go Slow online workshops that take place through Google Classroom. You can join with your personal Gmail accounts. If your G Suite admin will check the “Which classes can users in your domain join” option “Any G Suite class” then you can use your school account for the Go Slow online workshop training.