One of the commenters indicated that FB took down that page for being "violent in nature" (details not provided) -- not simply for its pro-GMO/Vaccine stance.
Disclaimer: I know noting about this particular case.
It is possible to fool FB into removing a page or some content. One way that is sometimes attempted (with some success) is to spam the comments on the page with objectionable content (hopefully goading other people to respond in kind) or (if it's an open group) join it and do the same. Then have other people report the page.
Also, simple misunderstandings happen. E.g. a post gets removed due to being threatening; in fact the post was just citing a threat allegedly made by an official. This seems to be even more likely to happen if many people report that content as objectionable: thus, people opposed to some organization/idea organize into mobs that report related posts as being objectionable.
This depends on the throughput of spamming that's going on. The throughput can be quite large if there's a significant amount of people cooperating. Also, this means that admins have to spend a nontrivial amount of time on such work on every single day.
The examples I know of are groups of political movements that have a lot of haters, so that might be somewhat of an edge case.
The page in question appears to be back online [1].
I suspect that, when you're dealing with what must amount to tens of millions of reports a day from users, mistakes are made. Thankfully, it seems like this one was corrected.
"Facebook bows to anti-science activists, shuts down ‘We Love GMOs and Vaccines’"[1].
It seems like Facebook is playing both sides in this matter.
[1]: https://www.geneticliteracyproject.org/2016/08/04/facebook-b...