Hello Tyler Barnes,
Thank you for posting your query in the Microsoft Q&A community.
You will be prompted for consent once you turn on "Do not allow user consent" under Consent and Permissions for Enterprise Applications as you have explained.
To prevent this from happening, you can grant tenant-wide admin consent in Enterprise apps or the App registrations page for this application. By default, granting tenant-wide admin consent to an application allows all users to access the application unless otherwise restricted
Kindly click on the link below to see the steps to grant tenant-wide consent for each application
However, when you grant tenant-wide admin consent to an application, you give the application access to the permissions requested on behalf of the whole organization. Granting admin consent on behalf of an organization is a sensitive operation, potentially allowing the application's publisher access to significant portions of your organization's data, or the permission to do highly privileged operations.
So be sure of the application before proceeding.
Also, you can grant consent to each user. Follow this link to learn more
Let me know if further assistance is required.
Babafemi