Further if Europe can ask for info to be censored what happens when 100 other nations ask the same for their own reasons. Will the search index be composed only of data that is acceptable to all parties?

When EU dictates what can be in the search index it is "right to be forgotten".

When China or Russia does it, it's at least "censorship", and probably also "dictatorship".

Well, Google already left China.

Yes, that is a foreseeable outcome.

But Google would probably say "no" to many of them.

Even if Google can resist the EU about global censorship, small search engines can't afford to.

Or they just don't do business in the EU. Lots of US businesses (and, for that matter Chinese, Japanese, etc.) just do business in their home countries. To the degree the EU makes it too difficult for certain types of businesses to operate there, they won't. It's a big market but it's not that big. If businesses can pull out of China because they can't reasonably operate there, they can pull out of Europe.

True.