Properly, it’s “Illinoisans” (example) but most people would just say “people of Illinois” or something similar. I pretty much only see it in print, very rarely spoken.
“Illinoian” is listed at that Wiki link but, in practice, is primarily a geological term.
Technically a Washington resident is a Washingtonian but you never hear that in public; whether it’s too easy to confuse with DC or because this state has very little that’s distinct from its neighbors I’m not sure. You are much, much more likely to hear someone call themselves a “Northwesterner”.
I was in Boston’s Logan airport today in Terminal A to send my daughter down to Dallas to see her grandparents. They had loud announcements that you are in the "Hub of the Universe’ which Boston proudly proclaims over and over using different formats. You can bite my ass on that.
I have gotten much better job offers in Texas with a much lower cost of living than I could possibly have here plus much shorter winters. I can’t take them right now for personal reasons but I will when my daughters graduate high school. I am thankful for the quality of the extremely segregated public schools my kids attend but, at some point, they are going to need to mix with the masses.
I have already explained to both of my kids that they are Massholes through no fault of their own but they will have to do better when they step into the wider world.
Whether because NYC casts a big shadow over the northern and western parts of NJ and CT, or because coincidentally their demonyms don’t roll off the tongue, I relatively rarely hear people call themselves New Jerseyans or Connecticuters.
On the former though Jerseyman was another term, for example used by NJ regiments in the Civil War, archaic now.
I was surprised to learn (when I moved to Utah) that this was the standard term. It looks as if it’s missing one or more letters, but that’s the standard form. Out-of-staters tend to add an extra letter between the “h” and the “n”, regardless.