There is nothing new about this. Putting a proxy into to modify content is as old as the usage of tcp proxies. What is new here is that they have no shame -- I don't expect software from a reputed company to pipe my email through their servers.
To play the devil's advocate, how is this any different morally from what Gmail (and Outlook, and Yahoo) do with their external emails feature? In each case, you give them the credentials for your other account, they pull the mail and display it in their interface (which, presumably, adds some new features that doesn't exist in the other account. Like conversations and tags.) LinkedIn is doing pretty much the same thing.
Everything they do differently is irrelevant as long as the user is asking them to do those things. If Gmail starts showing me fetish porn that's bad, if a fetish porn site does the same thing it's fine.
The only relevant difference is security/privacy, in which Google may be more trustworthy but even that is debatable, regardless of which side of the debate you land on.
