I get the same error with Firefox, and looking at the Advanced tab on the warning, it is telling you that it doesn't recognize the issuer of the Security Certificate. The "https" part of the web address means your connection to this site should be encrypted and safe, but Firefox can't be sure because of the fault with that Certificate. The risk to you here is that information being sent between you and this website might be visible to bad people trying to intercept that traffic. If you are exchanging any sensitive information (Social Security Number, etc)... you definitely want to think about this before continuing. If you ever see this warning when connecting to your bank... again, stop and think.
Is this problem with Firefox, or with the state website? It's hard to be sure, but I'm glad you were attentive to this warning. Don't ever dismiss something like this out of hand... it is trying to protect you. And I agree with you that your state government should be safe. But every business, state and federal governments, and anyone else can have an issue with their security... a hiccup, a misconfigured server, a Certificate that expires and was not renewed promptly. Stuff happens (or something like that).
So, what about options? I run 3 different web browsers fairly regularly. Firefox (my favorite), plus Chromium (the open source basis for the Google Chrome browser), and one more called
Vivaldi. You could install Google Chrome too, if you want that, but personally I try to avoid Google (though I can't seem to totally leave Google either). You can install Chromium from the Synaptic Package Manager by searching for "chromium-browser" or from the terminal with
sudo apt install chromium-browser
. Vivaldi is also available in Synaptic Package Manager (search for vivaldi-stable) or you can download the .deb file from their website.
You don't have to install these other browsers... just something to consider. It might be a good time to learn how to install software from the Synaptic Package Manager.
But where I'm headed with all this (I know, c'mon Stan, shut up already!).... is that Vivaldi and Chromium will both load your state government website without the Certificate error you see with Firefox. So these two browsers trust the Certificate Issuer, where Firefox does not. Who knows best? I don't know myself, but in a case like this, I would rather use a browser that is telling me that the https encryption is safe.