My understanding is that the skill books are only supposed to apply a bonus to the character holding them.  So if you have a navigation book bonus, it applies to you.  But if you appoint a Navigator because that character has a better navigation score than you do, they must also carry the book in their inventory to get a higher bonus, otherwise the bonus only applies to you if it's in your inventory.  So if you have a score of 30, and your appointed Navigator has a score of 50, and you have a +10 book for navigation, the displayed navigation score will not show a bonus unless you give the book to your Navigator.

For ERAS, I loaded a game and demonstrate that it works as intended:

My character has a grappling score of 40, with no grappling skill books/items.  My Bosun has a score of 59, plus several grappling skill items of +10, +10 and +30, stacking to +50 bonus.  On the character screen, under my character, there is a green (+60), indicating that I have a 100 score for grappling because my bosun's score is 100 (59 skill, plus 41 bonus...max score is 100, so the +50 in bonus maxes him out).

Also, there is a mod option to cap bonus item stacking, so make sure that value is off/on, depending on your preference.