"The IRS allows a sole member LLC to file schedule C"

It's a Requirement. Not "allows." The Feds don't recognize Single-member "LLC" entity type and it is treated as disregarded.

"If the LLC is a disregarded entity for federal income tax purposes, so that its income, deductions, and other items are reported on the federal income tax return of its owner, its income, deductions, and other items will be reported on the Illinois return of its owner. The LLC has no Illinois income tax filing requirements. For example, if the LLC is treated as a sole proprietorship for federal tax income tax purposes and its income is reported on its owner's U.S. Form 1040, U.S. Individual Income Tax Return, for Illinois purposes the LLC's income will be reported on its owner's  Form IL-1040, Illinois Individual Income Tax Return."

Here: https://www2.illinois.gov/rev/questionsandanswers/Pages/604.aspx