So the Adobe app works perfectly fine on macOS Tahoe while LuLu is disabled, or if Internet is disabled. As soon as I block any connection for the app, it is destined to close 20 seconds~ after opening it. It doesn't crash it just prompts the app to close and asks you if you want to save changes to your document or close without saving, no cancel option or nothing.
It happens also with After Effects and Premiere even quicker I think. I tried reinstalling older CC 2024 versions I've been using on other macOS versions and the same happens.

What should be the safest approach to take in the meantime? Keep LuLu completely off while using Illustrator? (and other Adobe apps). Or is it safer to edit the Illustrator rule to "allow" instead of "deny"? That way other apps like Creative Cloud stays blocked I guess. I also have Adobe telemetry URLs blocked on hosts, the updated list by Ignacio Castro's github.