Am I required to participate in Illinois Shines if I want to install a new solar photovoltaic system on my property?

No, you are not required to participate in the Program.  You can indicate to your installer that you do not wish to participate in Illinois Shines; additionally, if you want to keep the RECs from your PV system or sell them outside the Illinois Shines program, you can seek to negotiate that with your installer.  However, the funding available through Illinois Shines is likely to make a system installed under the umbrella of the Program more affordable than if not.