I live in Illinois can a girl age 8 and a boy age 3 legally share a bed room.

There is no "law" there may be rules of an apartment complex, if you are being investigation by children and family services they will have their regulations and opinions of their inspectors.
If you are in the middle of a child custody fight they may use this in court and hope the judge has issues personally.

So I guess what is the issue to make you ask ?

There is no law against it. It might be frowned upon by some but no it is not illegal.

In general terms at those ages there is nothing wrong with it. As the children get older then it may have to be delt with and they are split apart. But at this stage and for a few more years its not really an issue.