I doubt I could even find a company that prohibited accessing LinkedIn from a work computer anymore. Many don't disallow installing software either.
If you truly believe what you wrote, you almost certainly believe accessing work email from a personal device is prohibited at typical companies. Maybe this is true at large companies, but not anywhere I've worked.
Your argument has no validity. You claim that it's absurd for IT to differentiate between "sending your email to your phone" and "sending your email through a third party with no connection to email deliverability and no business relationship"