I am an adjunct instructor in a library science program.
We were having a discussion regarding patrons with body odor or heavy smells (such as perfume or cigarette smoke). What really surprised me…. several of my students who work in public libraries said they have an official policy that patrons who smell are not allowed to stay and are to be asked to leave the library. This really surprised me. Legally is this allowed? Who is to decide what an acceptable/unacceptable level of smell.
Overall, I found the notion of kicking out patrons because of smells to be repulsive, disgusting, and a completely against WHY we exist. If this is legal, I want to know how a library could, in good conscience, do this…
There is a large array of case law, academic articles, industry guidance, and news coverage on the subject of regulating smells in libraries (specifically, the smells of people and/or their belongings in libraries).
Based on those materials—and in particular, the case law—my answer to the question "legally is this allowed?" has to be: YES. With a carefully considered policy, carefully followed, barring library patrons based on their "disturbing" odor has been ruled to be legal, just like barring other factors that disturb the operations of the library (noise, eating, running) can be.
But just because a library can bar "disturbing odor" doesn't mean I always advise my clients to do it.
Why? Because this is 2020.
In 2020, we know that the impact of barring people based solely on them being "disturbing" is fraught with risk, both for legal reasons (claims based on the First Amendment, equal protection, due process, disability, etc.) and for reasons related to a library's mission (concerns related to the type of existential considerations raised by the member). 
Of course, in 2020, we also know that regardless of where you land on the question of "disturbing odor," this issue poses concerns from the other side, as well; a patron or employee trying to access or work in a library may find a smell (whether caused by another person, or by a condition of the building) to present an actual risk to their health (allergies, chemical sensitivities). So one person's access to the library may pose a risk to the access of another.
Finally, in 2020, while nothing is a sure bet, it is reasonable to expect that one of these days, one of the legal cases challenging a library's bar to access based on a "disturbing odor" is going to result in a policy or ejection being overturned. And while that currently-hypothetical case may turn on circumstances unique enough to not bar all such policies, such a ruling could throw the current legal footing into question.
Which is why I offer this: rather than barring people due to "disturbing odor" (which as the member points out, is a conclusion rooted in subjectivity) a library might be wise to consider planning, policies and action to:
It is this last bullet—related to safety—that I would like to dwell on.
Some smells are just that—smells. They may be perceived negatively, and perhaps even as a disruption, but to most people, they pose no risk.
Some smells are not just smells, but "tells"—byproducts indicative of conditions that are experienced by the individual carrying them (like it or not, we all have these). Some may be linked to a medical condition or disability, but in no way do they pose a safety threat to others. Many people who are perceived as "smelly" have "tells".
And finally, some smells are indicative of a potential health hazard to those in their proximity; for example: sulfur added to otherwise odorless natural gas, the odor of certain paints as they dry...or the smell of a staph infection in an open wound. These "evidence of danger" smells are the ones that libraries, who are legally obligated to provide their patrons and employees with a safe environment, need to be concerned about, and should develop policies to address.
Need an anecdote to distinguish the smells from the tells from the hazards? Here's a scenario:
A man walks to the library. While walking, he treads in dog poop.
Because decades of smoking cigarettes have dulled the man's sense of smell, he does not notice that his shoe is coated in poop. However, as soon as he enters the library, a page smells the poop, and points out to the patron that not only is his shoe smelly, but it is leaving fecal residue on the floor.
Because there are many health-related reasons why the library doesn't want dog poop on its floor, the man is asked to leave until his shoe is poop-free. The man leaves the library and visits his buddy across the street, who lets him hose off his shoe in the back yard.
When the man returns to the library, he shows the page the clean shoe, and it is clear that the dog poop has been eliminated. However, dog poop being what it is, the smell lingers on the shoe. But insofar as the library is concerned, it no longer poses an active hazard to toddlers crawling on the Children's Room floor. The man is allowed to walk into the library, selects the latest John Grisham novel, and leaves, the odor of dog poop lingering in the Circulation Desk breeze.
And that is the difference between using a smell to mitigate a health hazard, and tolerating a potentially disturbing odor in a library. It is also how a library focuses on providing access and a safe environment for patrons and employees—while avoiding judgments rooted in subjectivity.
In posing this question, it is clear that the instructor is thinking about mission, about a library's role in its community, and about optimizing access to resources for all. But the instructor has also honed in on this "subjectivity" concern, by asking: "Who is to decide what an acceptable/unacceptable level of smell"?
It is that very subjectivity that brings legal peril to the current scheme of things. Sooner or later, the right combination of circumstances will arise, and a judge will rule that simply barring someone from a library based on nothing more than a bad stink is a legal violation.
Therefore, as we move past 2020, and into an era that will, all signs show, be more in need of information access and authentication than any era previously, I offer this template policy to "flip the script" on how libraries address the issue of odor.
The ABC library is committed to access for all. With regard to odors in the library, this means:
We appreciate that as humans, our patrons bring a wide array of odors into our space, and not everyone appreciates that smell of others. If you need a scent-free area or well-ventilated area, please let us know. If you notice any odor or other factor that could be indicative of a health hazard, please immediately alert staff so it can be addressed per our policies.
Meanwhile, the library's Code of Conduct should state some version of: Any activity or substance posing a health hazard to patrons and employees is prohibited.
And finally, internally, I suggest this protocol for addressing reports of smells indicative of potential hazards:
Receive the report. Note the date, time, person reporting it, and what is reported. Ensure a qualified person immediately assesses the report. If there is a possible health hazard, involve the appropriate personnel or outside resources to develop an immediate response/mitigation plan, with all due respect for safety, privacy, access, and due process.
And that's it. From where I see it, while the status quo is legal, the future of "The Great Library Smell Debate" can shift to focus on two things: access, and safety. Factors that are subjective or based on personal preference ("bad smells" causing "disruption") are currently legally valid, but there is the possibility of a successful legal challenge. If a library is concerned about the impact of such policies on mission, and wants to avoid subjective value judgments about smell, developing policies that focus on access and safety might be a more appropriate approach.
That said, to reiterate my honest answer to the question: right now, based on case law, "subjective" policies about "disturbing" odor, if narrowly tailored to serve a valid purpose, and executed properly, remain enforceable. But as I have outlined, they can pose a risk.
Make no mistake—sometimes odor needs to be addressed, and from many perspectives. But the law provides many options, and using a focus on access and safety is one of them.
Thank you for a thoughtful question.
 The most authoritative and influential are: Lu v. Hulme (2015), Kreimer v. Bureau of Police for the Town of Morristown (1992).
 Trusting that an audience of libraries knows how to find research material, I'll simply say that the materials cited in the guide posted here (http://www.homelesslibrary.com/uploads/1/3/0/1/13014906/body_odor_handout.pdf) show the range of coverage and thought on this topic (at "Ask the Lawyer," we don't reinvent the wheel).
 This risk springs from the fact that, objectively speaking, every human being "stinks." Of course, for a variety of reasons, sometimes our personal odor is more overtly and broadly perceptible than at other times, and depending on an array of cultural or physiological factors, may or may not be welcome by them.
 For a thorough discussion of the mission-related considerations of imposing odor bans, I recommend the article "It is a Non-Negotiable Order": Public Libraries' Body Odor Bans and the Ableist Politics of Purity." By no means an unbiased academic exercise, you can easily tell where this author is coming from (they find odor bans antithetical to the purpose of libraries).
 These cases turn not only on precise wording, but on how the policy was applied, and the law in that precise locality.
 "Disruptive smell" while real, is, of course, subjective, since as I mentioned in footnote 3, all humans, to some degree, "stink," but "stink" is a relative term. In that regard, I am reminded of the classic scene in Frank Herbert's "Dune," when young Paul Atreides first arrives at the home of his future allies, the Fremen. Paul perceives their cavernous home, called a "seitch" as having a wretched stink, but just as he is about to show his disgust, his mother says "How rich the odors of your seitch..." saving her son from a fatal social blunder. Of course, they go on to not only get used to the smell, but to conquer the planet.
 By a variety of laws, which can include local health codes, OSHA regulations, labor law, union contracts, local law.
 What he actually says is "Um...sir? Hi, good to see you again. Hey, it looks like maybe you stepped in some dog poop?" Thank goodness, not all people talk like lawyers.
 I bet people who live near libraries collect stories like this.
 Some larger libraries, or libraries that operate in close relationship with municipalities, will have well-developed hazard response plans, which this protocol should fit right into. Others will not have that level of planning, or the resources to involve "qualified" internal personnel in assessing a reported hazard. For that, it is good to have a relationship with the local county health department.
 Can a person bring in a smell so foul and pervasive that, even if it doesn't cause permanent injury, can be considered a "hazard"? Anything that causes eyes to tear up/swell, retching, headaches, or violent coughing/sneezing in the general population can be considered a "hazard" (which is a term whose definition changes from law to law, but is used in its more generic sense here). But getting some back-up from the health department is a good way to ensure that you get solid confirmation of this.
 Have your lawyer review this policy no less than annually!