I did a test and cannot reproduce the issue you post.
Here are steps:
1.Set gmail.com as allowed domain in the SharePoint admin center.
2.Go to Active sites of SharePoint admin center -> Select the site -> Sharing -> Check whether has same settings as organization.
3.Share a folder with Gmail account by using specific link.
4.Log in Gmail with the sharing Gmail account in the Google browser -> Open the Sharing link from the email.
5.Log in sharing Gmail account -> Set the account in the Microsoft Authenticator app.
6.Re-open the Sharing link from the email -> Log in with MFA authentication -> Open the folder.
Please check following tips to troubleshoot the issue:
1.After setting the account in the Microsoft Authenticator app, close all tabs, then open a new tab or an incognito tab to open the sharing link.
2.Try to open the sharing link in the Google browser.
3.Try to share with another Gmail account, compare the result.
For further troubleshooting, please provide more screenshots about sharing steps and results.
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