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Dear Rikke,
Thank you for posting back. We appreciate your precious time doing tests and share with us the result.
Since we still didn't reproduce the issue when testing from our side, considering that you mentioned it doesn't save when others try to rate, it seem that other users in your organization have this issue. At the same time, more than one SharePoint list have this issue. In this situation, we suppose there is some background difference between your tenant and our test tenant.
The best way to troubleshoot the situation further is reporting it to the related team, they have higher permission to remotely assist you, they can also check your tenant environment from back end, collect logs when the Rating function has issue and then find root cause of the situation.
Microsoft 365 administrator has right permission to contact related team, therefore, we sincerely recommend you let your Microsoft 365 administrator follow steps in this article with admin permission, raise a support ticket and contact Microsoft related team.
For reference: How do I find my Microsoft 365 admin? - Microsoft Support
The support team has higher permission and more resource than us. This would be the most efficient way in handling this case for you.
Thanks for your cooperation and understanding!
We hope you stay safe and healthy.
Sincerely,
Tina | Microsoft Community Moderator