Is it legal to be fired over political views?

Illinois is at at-will state.  Barring an employment contract, a public-sector job, or a protected category, you can be fired for any reason (or no reason at all).

If you are not working for the government, yes. Private businesses (in the absence of discrimination against protected categories, such as religious or racial groups, people over 40, the disabled, etc.) have near-complete discretion over hiring and firing. (The prevailing doctrine is "employment at will," which is pretty much exactly what it sounds like.) They may fire people for any reason, at any time--including simply not liking the person, or his or her political views.