While it is true that the states may not violate the rights afforded to citizens of the United States, it was not always the case. The Civil War was fought in part about this matter of law with respect to abolition of slavery (The Union argued that states could not violate protections in the Constitution. The Confederacy argued that it could because the Constitution only listed the things the Federal Government could do. The 14th Amendment (one of three that were brought about in the aftermath of the civil war) was in part added to fix this problem (introduced by a read of amendments 9 and 10. I'm doing a TL;DR on the loophole but suffice to say, it's a bit of a weird explination).
That said, Rep Ingram is technically wrong, as everyone in the United States lives under dual sovereinties. This means that if you commit a crime in the state of Ohio that is also a crime per Federal Criminal Law, you are responsible for violating the law in both jurisdictions and could potentially face two trials for the same action (though this is rare, it's not unheard of). Murder is a great example of this because every state has at least case law crimilizing murder (as opposed to "Law on the books" codified law... case law is "Once upon a time, 12 people said someone was a criminal because he killed someone else. So everyone else now says they are guilty if the same circumstances are done by another person. Also... we only wrote down the laws of sentancing these people, not the legal definition of the criminal act) (Fun fact, a lot of Free Speech law in the United States is case law because it was determined by SCOTUS).
Any way, back to murder most foul. The feds can't try state crimes and states can't try federal crime. Murder is both a state crime and a federal crime. This means that the state of Ohio can hold a trial for a murder committed in the state of Ohio and the Department of Justice (federal) can try the same murder because it fell within U.S. Territory Holdings, specifically the state of Ohio. This does not violate Double Jeopardy because Double Jeopardy only stops the same court from hearing the same case about the same action. If a different court also has Jurisdiction, it can, in theory, also here the case as well, and punish according to their law. In practice, this is rare and Federal Government does have a policy that requires there to be a very good reason to try a suspect previously tried by a state (Usually, the charged crime is not the same. Frequently the Feds will try a criminal for a Hate Crime while a State where there is a different hate crime standard is lacking or the charge wasn't applied by the state. The Feds could also do this if they feel the state's sentence was grossly not severe enough (usually if the sentanced time by the state is half that for the Feds for one similar charge.
On the Flip Side, the Supreme Court has ruled that while States must comply with the protection of citizens rights compliant with the Bill of Rights, they ruled that there "Ain't no rule that a state can't protect rights not enumerated in the Constitution, or protect rights greater than those in the Constitution. Furthermore, the Constitution has exactly one criminal law in Constitution (Article III makes it illegal to criminlize Treason and requires at least two independent eyewitness to convict.). All the rests can only be violated by the government or an agent there. Most citizens will never do something that violates the Constitution and it only applies to what Government can or cannot due. Note the language of the First Amendment which begins with "Congress shall make no law..." and then lists a five topics of things they can't legislate about.
Compare to this, which requires teachers employed by the State to do a certain action or violate a law. Teachers, for example, are required to report all physical evidence of possible abuse they observe on a child to social services under penalty of law. This law would require teachers to respect all student religious practices in school under penalty of law. In the United States, education is a state level issue, not a Federal one. And the government, while in the role of an employer of government work, can restrict employee speech as if it was a private company not bound by the first amendment.
Thus, the Ohio Bill is not redundent because it is a law that restricts government employee's speech (Teachers opinions on religion) while they are "on the clock" as a condition of continued employment. Since the First Amendment doesn't protect political speech of government employees while doing work for the government, the Federal Government is not the government employing the teachers of Ohio, so they can't make a law telling Ohio teachers to respect religious practices any more than it can try an Ohio citizen for a crime that they don't have jurisdiction over (it's illegal in Ohio, but not in the United States).
So Rep. Ingram is wrong because the core issues' is not protecting the student's religious liberty (SCOTUS has ruled that students may engage in religious practices in school (with in reason) so long as it is not led by school employees (they may be required to act as a chaperone, but they cannot have a part in running the club or endorsing it). Rather, the law is that stating that the government is limiting it's employees own speech about their personal opinions on any and all religious subjects while they are working as employees of the State of Ohio through it's school systems.
This is neither a protection of the First Amendment (it's an exception) nor is it redundant (since Ohio state law is the highest law of the Ohio School system, rather than the U.S. Federal government. There's a specific clause in the Constitution that basically says "When in doubt about who gets a specific government power, assume it's the state unless the Feds meet some burden of proof that it's their power". Typically the Federal Government does not have any compelling reason to meddle in specific school systems in the United States.). The law is politely informing teachers that any discussion the superiority of one religious belief over another religious belief system while employeed is a violation of the law (likely a civil offense with the teacher's firing the likely outcome). Students on the other hand, are free to hold "My God is bigger than your God" style debates with their classmates when appropriate to hold such conversations.
As a whole, primary students First amendment speech rights are not nearly as protected when conducted through school related activities (Multiple SCOTUS cases on this) though they are fully protected for activities not related to school functions or affiliated with them, even during enrollment.