Can I still use Airport Extreme?

I have retired my older 2004 AirPort Extreme 802.11g (Snow Dual Ethernet) because later macOS Airport Utility does not support it and I don't want to configure it via a hacked app or via an old PowerBook G4 running OS X 10.5.8. And it does not support 802.11n.

On the other hand I have extended the mobile router's coverage via Ethernetted 2011 AirPort Extreme 802.11n 5th Generation and it works OK with current gear.

not unless it stops working

just because it's discontinued don't mean it will open all securely closed features to let all in

if a serious security issue show up they will likely release an update

the people who pursue finding exploits in internet equipment, usually spend their resources on very widespread equipment, apples routers never really had that big a market share I believe.

The short answer is maybe.

A bit longer one would have you answering the following four questions:

1. Is my current networking hardware working?
2. Does my current networking hardware meet all of my networking goals?
3. Is network security important to me?
4. Do I need to take advantage of newer networking technology?

Obviously, if you can answer "yes" to the first two, then there is no need to rush out to replace your AirPort Extreme base station. If you also answer "yes" to the third and/or fourth ones, then that would be a consideration to pursue a replacement.

... and, if you are considering a replacement, what you would replace it with will also depend on your "comfort level" with networking technology. ... and, by that, I mean do you want simple "set it and forget it" or the ability to "fine-tune" your network?