I agree that it sounds ominous, at first I was put off, but then I remembered any app I've ever used on facebook that said the same thing. It doesn't let them hack the account or get any personal info from you, it just integrates your account into their system. That's all it does.
Have no fear! Most people with twitter have linked up and it's all fine. I have, and I've had no problems. It's in your best interest to go ahead with it! People get to know you as a person. I'm certainly more inclined to buy from people when I know who they are. Since I joined twitter, I've gotten to know 2 people more and for that reason I'm buying from them, when before I might not have. I know them more, I know their products better, and I can see that it really is an extension of who they are.
It'll help, and it's worth the ominous-sounding-but-actually-perfectly-safe message you get prior to authorising it.
And all the "post tweets for you" and stuff just means you can enable a feature to automatically tweet if you list or renew an item (though I wouldn't use that feature if I were you, it seems a little spammy to your followers, especially if you renew frequently). And it doesn't actually add new people for you to follow, it just suggests them based on other Etsy users who have enabled it.
Hope this helped.