Backing up home directory, can I exclude ~/Library?
The Library folder contains all the preferences set for the applications you are using, login information for Mail etc, the local mail archive, your keychain and a lot of other configuration stuff. If you are using iCloud Drive it also contains the local copy of the drive content; and backups of your iDevices in case you don‘t use iCloud backup for them.
You may be able to recover most of it in case of data loss, but some things (e.g. your keychain or any locally stored mail) will be lost.
Given that external drives and USB sticks are rather cheap nowawdays it's most probably not worth the pain to fine-tune a backup script to include just the essentials from ~/Library.