It's pretty trivial to write an extension that will quickly let you copy some fields in a LinkedIn's page and paste it into a CRM tool.
To get full name via jquery for example
fullname = $('#name').children('h1').eq(0).children('span').eq(0).children('span').eq(0).text()
However, is this against Linkedin's terms of service? I have read it and it says scraping is forbidden, but is this scraping? It's merely automating copy pastes for data on a single page I have access to.
Edit: To further clarify. This extension will only let you automatically copy text you are already seeing on an open Linkedin profile page you have acces to, into a CRM program that you use. It would automate the exact equivalent of: opening the Linkedin page, selecting certain text like name and email, COPY, opening CRM program, selecting respective fields, PASTE.
Yes, LinkedIn does not allow scraping of public profiles.