Yes, we do have copyright clearance. In most cases, we purchased from the creator the right to post the content, or in some cases, our excerpt falls under "fair use" provisions of U.S. copyright law (explained below).
Copyright laws protect the integrity of intellectual property, protect the creator's right to control the usage of that property, and protect the creator's right to profit from that property.
U.S. copyright law also recognizes that the Constitution also protects the freedom of speech, so there are important exceptions to copyright protection that allow others to make "fair use" of intellectual material they didn't create.
Nonprofit educational institutions, including churches, typically, get a little more latitude on what can and cannot be done with intellectual property, but if you are sued, the courts ultimately decide.