You could use Google to find articles published by conservative US think tanks, like the Hoover Institution or The Heritage Foundation. It actually turns out, though, that they haven't published much about libraries.
From 1997: "Of all the great American institutions that deserve the support and affection of conservatives, lending libraries are among the most essential. At their best, libraries are repositories of our national intellectual heritage. In the free market of ideas, libraries are like banks, where any American can borrow the accumulated capital of knowledge and where some will eventually deposit the dividends of discovery. The cause of conservatism has everything to gain from this egalitarian preservation of political philosophy, classical literature, moral fiction, historical fact—of "the best that has been thought and said," as Matthew Arnold had it." but also
"The nation’s libraries do a poor job of preserving conservative truths. We need to start our own." http://www.hoover.org/research/virtual-veritas
Also from 1997: "Public libraries are becoming de facto pipelines for pornography on the Internet. Ask the library whether it blocks pornography with filtering software; if not, establish family rules about using computers with Internet access at the library." http://www.hoover.org/research/home-front-1
From 1997: "Of all the great American institutions that deserve the support and affection of conservatives, lending libraries are among the most essential. At their best, libraries are repositories of our national intellectual heritage. In the free market of ideas, libraries are like banks, where any American can borrow the accumulated capital of knowledge and where some will eventually deposit the dividends of discovery. The cause of conservatism has everything to gain from this egalitarian preservation of political philosophy, classical literature, moral fiction, historical fact—of "the best that has been thought and said," as Matthew Arnold had it." but also "The nation’s libraries do a poor job of preserving conservative truths. We need to start our own." http://www.hoover.org/research/virtual-veritas
Also from 1997: "Public libraries are becoming de facto pipelines for pornography on the Internet. Ask the library whether it blocks pornography with filtering software; if not, establish family rules about using computers with Internet access at the library." http://www.hoover.org/research/home-front-1
The Heritage Foundation praises Andrew Carnegie's privately-funded public libraries here http://www.heritage.org/markets-and-finance/report/free-mark...