Hi Philip,
Generally, rules are not disabled when opening Outlook in safe mode. Have you checked if your rules are enabled from Tools > Rules and Alerts? Make sure the check boxes before your rules are selected.
Do these rules work if we manually run it via clicking the 'Run rules now' button?
Based on my research, rules not working issue may happen due to a corruption within the rules or within the mailbox. It could also happen if the Send/Receive file (.srs) file is corrupt.
If this is the case, we may try using the Inbox Repair Tool (Scanpst.exe) to scan and repair your Outlook data file to see the result. For your reference:
https://support.office.com/en-ie/article/Repair-Outlook-Data-Files-pst-and-ost-64842a0a-658a-4324-acc6-ef0a6e3567cd
If Inbox Repair tool doesn't work, please also try recreating the Send/Receive file (.srs) file and then test it again. To do this, exit Outlook and find the Send/Receive file (<profilename>.srs) file from the following path:
C:\Users\%username%\AppData\Roaming\Microsoft\Outlook
Rename the <profilename>.srs file to <profilename>.old, and then restart Outlook to see the result.
Please let me know the result.
Regards,
Steve Fan
TechNet Community Support