That's the 'establishment' clause. Assuming that a correct reading of the 14th does oblige the States to comply with the 'establishment' clause it still says 'Congress shall make no law' not 'Judges shall place no monuments.' No law was made by doing so therefore the 'establishment' clause is not applicable in the furthest stretch of the imagination unless the true meaning of 'is' is "anything I say it means."
If that is the case then we most definitely have the rule of men instead of the rule of law. If we are going to live by the rule of men then I am going to be a man who sets the rules. How big is your arsenal and how good are you with it?
BTW, the notion that, because of the Fourteenth Amendment, states are bound by the provisions of the First Amendment has also served as the foundation for some conservative legal arguments. For example, in 2000, the Supreme Court used the same principle when it told the State of New Jersey that the state could not require the Boy Scouts to hire gay scoutmasters because that would interfere with the scouts' First Amendment "rights of association." See Boy Scouts of America v. Dale (2000).