The advantage of of having the +1 button in the browser is so you can +1/share sites that don't include the +1 button themselves.
> But the +1 button extension will send every page you visit back to Google, with your unique user id as part of the information sent back
There is now way to know if you have +1'd a page without sending your unique id with. A button that doesn't tell you if you have +1'd something isn't very useful and you will continually be +1'ing pages over and over again.
> This is just insane. There is absolutely no reason for this information to be sent back, and it is completely identifiable and all in plain text. The installer says that it can access all your website data, not that it does access it and sends it back to Google.
If an extension has permissions to access "your data on all websites" there is no way to prevent it from also sending your data to all websites. HTTP is request and response and not very useful with only one or the other.
The Chrome Web Store says
"THIS ISN’T THE USUAL YADA YADA!
In addition to the practices described in the Google +1 Button Privacy Policy, by installing this extension, all of the pages and URLs you visit will be sent to Google in order to retrieve +1 information."
The install page linked to from the blog post should be more clear about what the +1 button sends to Google.
None of your data is sent in plain text however. It is all over SSL to https://clients6.google.com/rpc.
> I removed the extension immediately.
Good for you. No one is forcing you to use it.