"shouldn't" doesn't count (isn't good enough). And depends on _exactly_ what you mean by 'inactive'...
I had a mobile workstation and had issue with simple 1080p streaming due to the security software on the system. A much lower-end system did fine. The security software itself wasn't the issue, it was the security teams approach for general end-user machines conflicting with the requirements of livestreaming.
Multiple security software stacks... unfortunate reality in many circumstances
Multiple antivirus software installed ... a sign, usually, of a completely screwed up environment (though possible on certain, non-overlapping functions enabled, but still bad practice). If what you are doing is 'corporate endorsed'' (ie leadership of this larger network), then time to get Desktop Support involved to configure the security tools to not interfere (and that may or may not be easy to do, hence needing leadership support, as IT Security Team will most likely need to make some exceptions for your system)
Depending on use case, I'd be inclined to start with a dedicated streaming computer, otherwise locked down.
- This will make IT Security team more comfortable that the exceptions being granted won't cause vulnerabilities in other typical end-user activity (email, web browsing, etc)... but, depends on circumstances
However, that appears to be a 12-yr old CPU. Do you have a SSD, or HDD? Realistically, I expect you are bottlenecked somewhere.
Try again with 30fps, not 60. Monitor hardware resource utilization (CPU, GPU, RAM, Disk I/O etc,)