Err… ish. That’s kind of sensible advice, but in context bordering on bullshit. All IP addresses in nmcli device show will be link-local, and literally useless to anyone not on your LAN (and people on your LAN can just listen for ARP broadcasts to get the same information).
Caveat maybe if you have valid IPv6 addresses, but that’s both quite rate and networkmanager generates new ones on boot by default anyway for privacy reasons, so those are also mostly useless.
Unless you’re working on a router or have your laptop plugged straight into a modem, you don’t have to worry about this.
So, yeah, not sharing that could be sensible advice if you lived in the year 1980, and just bought your first internet connection with a freshly minted IPv4 address. In the modern world it’s almost certainly rooted in misunderstanding networking, though.
That said, if you are really unsure that you’re not on some super weird connection, you can check this wikipedia page - it has a list of all special address ranges with information about them - anything that says “local”, “private” and such is always safe to share. Refer to the descriptions for other contexts (if you, say, somehow got something from the military-reserved IP address range, maybe don’t share your IP address).
Take as an example my eno1, all of these addresses are in the 192.168.0.0/16 block, and hence only accessible on my LAN. The fe80:: IPv6 address is the link-local address, and also not accessible elsewhere. Depending on what block your router chooses, and how its dhcpd assigns addresses, you in fact might have the same exact IP addresses on your device:
GENERAL.DEVICE: eno1
GENERAL.TYPE: ethernet
GENERAL.HWADDR: 18:C0:4D:39:64:87
GENERAL.MTU: 1500
GENERAL.STATE: 100 (connected)
GENERAL.CONNECTION: ethernet
GENERAL.CON-PATH: /org/freedesktop/NetworkManager/ActiveConnection/5
WIRED-PROPERTIES.CARRIER: on
IP4.ADDRESS[1]: 192.168.8.193/24
IP4.GATEWAY: 192.168.8.1
IP4.ROUTE[1]: dst = 192.168.8.0/24, nh = 0.0.0.0, mt = 100
IP4.ROUTE[2]: dst = 0.0.0.0/0, nh = 192.168.8.1, mt = 100
IP4.DNS[1]: 192.168.8.1
IP4.DOMAIN[1]: ts.net
IP4.DOMAIN[2]: lan
IP6.ADDRESS[1]: fe80::bd95:d202:3bc0:9b25/64
IP6.GATEWAY: --
IP6.ROUTE[1]: dst = fe80::/64, nh = ::, mt = 1024
IP6.DNS[1]: fe80::9683:c4ff:febd:813c
The only arguably problematic address is the HWADDR, because that can uniquely identify your network chip, but it cannot easily be used for anything since it’s not exposed on the IP layer. The worst we can do is link a specific purchase to you if we worked for the manufacturer of your chip, or tell you which chip it is.