How to integrate external user tables with WP?

This seems pretty tricky and it depends very much on your needs. You could either alter the WP database on each install or make 1 3rd party database along with a script that registers them on the WP install and sets their permissions. The 2nd solutions seems better for me.

Create a database where you add each user with a row for each WP install where you specify their permissions.

Let’s say you have the following permissions: subscriber, contributor, author, editor, admin. Make a database for each user and set their permission. Make a 3rd party script which registers them to the WP installs and sets their permissions. When you change a permission, query the WP installs and update it there.

You will need mostly the WP Database description and wp_update_user function.