Unless someone can point to a piece of STATE level legislation authorizing the prohibition on the possession and / or carry of a firearm in a PUBLIC Library in the State of Utah it would be a violation of STATE LAW to enforce such ban or policy!
Please see:
http://le.utah.gov/~code/TITLE53/htm/53_05a010200.htm
53-5a-102. Uniform firearm laws.
(1) The individual right to keep and bear arms being a constitutionally protected right under Article I, Section 6 of the Utah Constitution, the Legislature finds the need to provide uniform civil and criminal firearm laws throughout the state.
(2) Except as specifically provided by state law, a local authority or state entity may not:
(a) prohibit an individual from owning, possessing, purchasing, selling, transferring, transporting, or keeping a firearm at the individual's place of residence, property, business, or in any vehicle lawfully in the individual's possession or lawfully under the individual's control; or
(b) require an individual to have a permit or license to purchase, own, possess, transport, or keep a firearm.
(3) In conjunction with Title 76, Chapter 10, Part 5, Weapons, this section is uniformly applicable throughout this state and in all its political subdivisions and municipalities.
(4) All authority to regulate firearms is reserved to the state except where the Legislature specifically delegates responsibility to local authorities or state entities.
(5) Unless specifically authorized by the Legislature by statute, a local authority or state entity may not enact, establish, or enforce any ordinance, regulation, rule, or policy pertaining to firearms that in any way inhibits or restricts the possession or use of firearms on either public or private property.
(6) As used in this section:
(a) "firearm" has the same meaning as defined in Subsection 76-10-501(9); and
(b) "local authority or state entity" includes public school districts, public schools, and state institutions of higher education.
(7) Nothing in this section restricts or expands private property rights.
Renumbered and Amended by Chapter 382, 2008 General Session
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and further:
http://le.utah.gov/~code/TITLE76/htm/76_10_050000.htm
76-10-500. Uniform law.
(1) The individual right to keep and bear arms being a constitutionally protected right, the Legislature finds the need to provide uniform laws throughout the state. Except as specifically provided by state law, a citizen of the United States or a lawfully admitted alien shall not be:
(a) prohibited from owning, possessing, purchasing, selling, transferring, transporting, or keeping any firearm at his place of residence, property, business, or in any vehicle lawfully in his possession or lawfully under his control; or
(b) required to have a permit or license to purchase, own, possess, transport, or keep a firearm.
(2) This part is uniformly applicable throughout this state and in all its political subdivisions and municipalities. All authority to regulate firearms shall be reserved to the state except where the Legislature specifically delegates responsibility to local authorities or state entities. Unless specifically authorized by the Legislature by statute, a local authority or state entity may not enact or enforce any ordinance, regulation, or rule pertaining to firearms.
Enacted by Chapter 5, 1999 General Session
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any questions?