"Custom library" is too broad a category to be useful. Libraries that reimplement functionality that's standard in the JRE, such as the Collections API, are almost certainly useless, and probably did more harm than help in an educational setting. However, there are a large number of tools, particularly Google Guava (enhanced collections like multisets and bimaps), the Apache Commons tools (including string parsing, hashCode
building, and the like), slf4j/log4j for logging, and runtime environments such as Spring that are basically standard in the industry.
The general principle is "don't reinvent the wheel". If you have an example class out of a textbook that gets a basic job done that isn't in the standard API or one of the de facto standard third-party libraries, by all means use it, but don't prefer some professor's half-baked and untested implementation to ones that have been in use by thousands of developers for years.