Hello Lucasso,
We apologize for the inconvenience caused, as per the description above, you are not able to sign a PDF file using the CAC digital certificate, Is that correct?
Using Adobe Reader, only PDFs with Reader Usage Rights enabled (through Acrobat software) can be signed using a digital ID.
Assuming you are using freeware Adobe Reader to sign the PDF file as I have checked the records with your current Adobe ID(email) and could not find any Acrobat license registered.
Try resetting Adobe Reader's Preferences once and reboot the machine, to reset the Preferences, please refer to the article How to reset Acrobat Preference settings to default.
Try disabling the Protected Mode once from Edit>Preferences>Security(Enhanced)>uncheck "Enable Protected mode at startup"
Note: Disabling the protected mode is only for testing purpose, please enable it back. Protected View feature for PDFs (Windows), Adobe Reader
If the issue persists, remove Adobe Reader using Acrobat cleaner tool Download Adobe Reader and Acrobat Cleaner Tool - Adobe Labs
Reboot the machine and install the latest Adobe Reader from Adobe - Adobe Acrobat Reader DC Distribution
You may also refer to the following Adobe article and discussion Reader DC won't accept digital signature from smart card reader
Certificate-based signatures, Adobe Acrobat DC
Let us know how it goes and share your findings.
Regards,
Anand Sri.
[Edited response]