Over 500 million people trust Google with complete and indefinite access to their email. The leap from trusting no external email providers to trusting Gmail is much greater than this incremental step of trusting LinkedIn as well. The risk is similar to trusting an established company to automatically backup your emails, and smaller than trusting startups like Greplin (which rebranded and got acquired) to safeguard a dump of all your emails.
This is not to say the privacy and uptime risks are non-existent: the attack surface area is marginally increased and there is another system that could break.
Claiming LinkedIn's doing a "MITM attack on your email" is on the same level as saying "Google is Big Brother." Both statements capture an element of reality, but with an extremely alarmist bent.