One of the chief arguments against restricting content is because libraries are funded by extortion. We need to maintain a collection that served the entire community robbed by the state, not just specific interest groups.
Additionally, there is a fundamental disconnect between what we are taught about the nature of government and the reality. The myth of a democratic republic with a state subservient to the people is a nice story, but not how power works. There is no inherent rational or moral authority in majorities or minorities. The State exists to perpetuate itself and enrich the political class, not to protect our rights and liberties.
As for taxes, government has never behaved as if tax revenue includes a responsibility toward the taxpayer. You have authority over how you choose to spend your money. You have no authority over how an extortionist spends what is extorted from you. Even libraries and fire departments, probably the two least-bad tax-funded systems people encounter, are built on this foundation. This is also why the government can get away with spending $160 per man, woman, and child on Ukraine, to say nothing of the "Just-Us" system, the War on Drugs, and innumerable other true injustices. No, the library has a few books we don't like, so that requires public outrage! And some of these clowns want librarians fined or imprisoned through that broken system because they think they can use it to impose their ideas.
On the practical front, when people get outraged over the library containing a book, the Streisand effect kicks in. Shelf space is always at a premium. We can't afford to keep books people don't read any more than a market-based store can afford to keep items on the shelf if no one is buying them. We may be disconnected from the market, but we have metrics for what stays. Instead of the natural cycle of unpopular fiction getting weeded out, these protests shine a spotlight on these books and guarantee at least a temporary resurgence in interest. I have never seen one of the challenged books circulate locally until people started pitching a fit. Now it is getting borrowed, which resets the clock on possible removal from the system due to a lack of interest. The protests are counterproductive when it comes to our collection policy.
Late additional thought: Take the 50 Shades of Grey novels as an example. Some people enjoyed them when they dropped, but I doubt anyone would cite them as great literature, and interest has tapered off. I'm not even sure my branch still has a copy on the shelf. No one has borrowed it in ages, so if it isn't already gone, it will probably be weeded soon. I'm sure one or two libraries in the district will keep copies on hand, but not every library will waste space even on the slimmer paperback editions. Trash doesn't last unless people pitch a fit. If these Karens were to (probably rightly) condemn trash literature like that, it won't get weeded. We may even need to buy new copies if demand spikes.
If we have no authority over what is extorted from us then the whole library debate is moot anyway as it is funded by money that is extorted from us.
I absolutely agree with almost everything you said above. It's just that I object to citizens expressing how they want their tax money spent (or not spent) being called "banning" anything or violating anyone's freedoms. No matter how dumb or ill-informed they might be. Like you said, you can do what you want with your own money and I don't care what books you buy. If you don't want nosy ass citizens worrying about what you read, don't make them buy your books.
I don't think it's necessarily a moot point. To the extent government extortion revenue gets diverted back to projects which actually serve the public, we must be good stewards of that money. And since our budget is entirely disconnected from the taxed individuals thanks to the fungible nature of money, we need to strive to ensure the entire community is served to the best of our abilities.
Of course the idea solution might look like a membership subscription answerable to the members directly, or a charitable trust fund functioning as a neutral service to all. Some libraries in the US are funded by these methods instead of property taxes. Homeschool associations and churches often set up libraries for their members informally, too. But while this is possible, the real hurdle is persuading people that it is the proper solution. In the mean time, getting mad about library books is a waste of effort when far greater injustices exist.