Correct, but in the Illinois State Constitution, there is a direct clause prohibiting government from giving special preference to any specific religion:
ARTICLE 1, SECTION 3. RELIGIOUS FREEDOM
The free exercise and enjoyment of religious profession and worship, without discrimination, shall forever be guaranteed, and no person shall be denied any civil or political right, privilege or capacity, on account of his religious opinions; but the liberty of conscience hereby secured shall not be construed to dispense with oaths or affirmations, excuse acts of licentiousness, or justify practices inconsistent with the peace or safety of the State. No person shall be required to attend or support any ministry or place of worship against his consent, nor shall any preference be given by law to any religious denomination or mode of worship.
~ (Source: Illinois Constitution.)
My point was the so often quoted phrase, “separation of church and state” does not exist in that word order in any law, amendment, etc. It is a phrase used by Jefferson. It is not a law. What you cite is similar to the first amendment. The establishment of a religion would obviously show favoritism.