Mojave OS Stealth mode: Is it compatible with Norton Security package?
Yes, enabling stealth mode on Mojave will not wreak havoc with Norton Security.

However note that enabling security features such as Stealth Mode or indeed the Norton Security Firewall itself does not magically give you "more security" or "better security". You'll need an understanding of what these features do or do not do in order to reason about enabling them. It might harm more than it helps in some cases.

Stealth mode works by blocking responses to ICMP ping packets as well as incoming requests for non-open ports. This means that you cannot ping the computer to get an immediate response, and if you attempt to connect to a service on the computer that is not offered, you'll not get a "closed" response, but instead nothing will happen.

The advantage is that if you have a scenario where you do not want others on your local area network to know that the computer is there or which services it provides, they could be "fooled" by not responding to these packages.

On a normal home user scenario the feature does not give you any additional advantage against probing from the Internet at large. It is only a protection on your local network. So if someone comes to your home and plugs in a computer into your local network, it will take them longer to map out which IP-addresses your computers have and which services they offer. In general, this is not a problem for home users at all.

In a mobile scenario where you take your laptop out in the world and connect to insecure (often WiFi) networks without forcing everything on a VPN, the feature does have some merit. Evil users on the same network cannot ping to discover your computers - although on wireless and especially wired networks, it is quite easy to discover your computer simply from the fact that it is itself sending out information onto the network. Similarly evil users will need more time to discover which services your computer offer.

The advantages of the feature are very limited for most users in most cases.

The disadvantages are mostly concerning "debugging" i.e. when "finding errors". If you for example try to connect yourself to the computer via a network service that isn't working for some reasons, you might find yourself waiting for timeouts, non-responsive programs, etc. - instead of having a quick error message popping up stating the cause of the interruption of service.