I have a form library in SharePoint Online, and would like to be able to use Quick Edit to update multiple items at a time. I have quick edit turned on, and am able to switch to that view. However, all of the fields are greyed out and cannot be modified. Are you able to use quick edit with form libraries that use InfoPath?
The InfoFath form implementation for a List/Library does not have any relation with Quick Edit functionality. Since you have already enabled Quick edit so you can simply edit fields properties similar to an excel file.
Regarding grey-out fields, you can verify if the field type is not "Calculated Field". Also, As I can see from the screen shot, Date field is not showing date-picker So you can try doing this in Internet Explorer browser.