You may be interested in IRA form 8282.
https://www.irs.gov/pub/irs-pdf/f8282.pdf
This form is used by charities to report when they dispose of large gifts that were previously reported by the taxpayer on form 8283. If the organization disposes of an item within 3 years of the date of receipt, they must report that to the IRS, along with an explanation of whether or not the organization's use of the item furthered it's exempt purpose or function. If an organization accepts your large donation on a form 8283 and you report it on your tax return, and then the organization disposes of the item in less than 3 years, this fact must be reported to you and the IRS and may trigger a requirement for you to amend your return due to the unrelated use rule.
Here, the key words are "describe how the organization’s use of the property furthered its exempt purpose or function." If a pet rescue charity accepts your donation of rare books, it would be hard to see how that donation would "further their exempt purpose or function" except by fundraising.
For an example of an organization that accepts an item the "furthers its exempt function" and then later has to dispose of it because its use became unfeasible, you can think about someone who donates a van to Meals on Wheels, where the charity plans to keep the van and use it for picking up and delivering food and meals. That would be a related purpose. If they were forced to sell the van after 6 months because the frame was rusted beyond repair, that would be a case where they had accepted the donation for a related purpose but were later forced to sell for other reasons. (In contract to the donation of, say, a motor cycle, where it could never really be expected to "further the exempt purpose" of the organization and was always destined for sale one way or the other.
Lastly, note that where form 8283 must be signed by an official of the charity, it is this official who must certify if the item will be put to a related or unrelated use. The official also agrees to file form 8282 if the organization disposes of the property within 3 years. So it is not you who decides if the use is related, it is the charity. (And the charity can lose their tax-exempt status if they abuse the rules.)
https://www.irs.gov/pub/irs-pdf/f8283.pdf
