Note how SB354 compares to SB1581, and you'll see that the phrase "or private or independent institution of higher education" was present in SB354 but not SB1581. That means that SB1581, as amended, makes no changes whatsoever to private colleges. It will still be illegal to carry on the premises of a private college, and private colleges may still adopt anti-gun policies.
SB354 wrote:A license holder may carry a concealed handgun on or about the license holder's person while the license holder is on the campus of an institution of higher education or private or independent institution of higher education in this state.
SB1581 wrote:a license holder may carry a concealed handgun on or about the license holder's person while the license holder is on the campus of an institution of higher education in this state.