McGrath of Harlow: "There's nothing any of us can do to stop all our threads being paraded on the nastiest sites and to the nastiest people on the net, at a touch of a button".
As a few people have already pointed out, this is entirely possible already. I suspect that anyone wishing to post a link to a Mudcat thread for nefarious reasons would already be capable of doing so without the aid of the 'share' button - it's an incredibly simple operation. And the idea that the new function allows sharing "at a touch of a button" is not entirely accurate - it still requires you to sign into the other site and then approve the link. A simple enough process, but no more so than copying and pasting the url directly, although I notice that if you post to Twitter the link is automatically generated as a "bit.ly" url, saving you the need to generate your own.

Lizzie Cornish 1: "By all means, share Mudcat around, but not like this."
So how, exactly? You either agree to participate and accept that your posts are available for anyone to read, share and comment upon, or you cease to be involved and "The Weird Ones" have won. If you mean "only share amongst friends and people who I know and trust" then it's an admirable sentiment but you may as well not share at all as you're simply perpetuating the sense that Mudcat is some kind of private members club.