Google Classroom only allows students to join. However, parents can be invited to receive weekly summaries. See below....
Before inviting a parent/guardian to receive summaries from Google Classroom, please verify that they have "Ed Rights." Only parents that have Ed Rights should be invited.
1. Run the "Parent Email List" report from TeacherVUE.
2. The report will list the email for each student's parent/guardian along with whether that parent/guardian has Ed Rights for the student. If you see a "Y" for ed rights, you can invite them to receive email summaries using the address shown. If you see "N" (like the last parent/guardian below) you can not invite them to receive summaries.
If the parent is signed in to Google/Gmail and they open an invite link that was sent to a non-Gmail address (@yahoo.com, @hotmail.com etc) the parent will see the prompt below.
If the parent wants to use a non-Gmail account, the solution is to open the invite link in a browser that isn't signed in to their Google/Gmail account. They will then see a success message like the one below.