I'll add that there is indeed a lot of wrong stuff in the EFF article. Don't get me wrong, articles 11 & 13 are indeed bad law (IMO), but promoting inaccurate information does not help.
For example, there is no mention of "noncommercial activity" in the entire text of Article 13 (non-commercial activity is only mentioned in one of the recitals for a different purpose). Article 13 applies to "online content sharing service providers". These are defined in Article 2:
"‘online content sharing service provider’ means a provider of an information society service whose main or one of the main purposes is to store and give the public access to a large amount of works or other subject-matter uploaded by its users which it organises and promotes for profit-making purposes.
"Providers of services such as non-for-profit online encyclopaedias, non-for-profit educational and scientific repositories, non-for-profit open source software developing platforms, as well as internet access service providers, online marketplaces and providers of cloud services which allow users, including businesses for their internal purposes, to upload content for their own use shall not be considered online content sharing service providers within the meaning of this Directive;"
Likewise, the following claim is misleading:
"Speaking of references: the problems with the new copyright proposal don't stop there. Under Article 11, each member state will get to create a new copyright in news. If it passes, in order to link to a news website, you will either have to do so in a way that satisfies the limitations and exceptions of all 28 laws, or you will have to get a license. This is fundamentally incompatible with any sort of wiki (obviously), much less Wikipedia."
Article 11 is about ancillary copyright; now, ancillary copyright is a bad idea, but the above is a misrepresentation. For starters, Article 11 (3) subjects ancillary copyright to the same limitations as regular copyright, in particular Articles 5 to 8 of Directive 2001/29/EC, including the right to quote such content (which in turn requires attribution).
What Article 11 does is (potentially) creating a copyright for small excerpts that might normally not be copyrightable and granting that right to press publishers in addition to the authors. This is a problem for news aggregators and search engines (which rely on producing content that's an aggregation of normally not copyrightable material) but not per se for Wikipedia (where pages consist of original material littered with references and quotes).
The biggest problem for news aggregators is that Article 11 (1) leaves the definition of "insubstantial" up to member states, which will probably lead to a "lowest common denominator" result, where the most restrictive interpretation by a member state effectively determines copyrightability for the purposes of ancillary copyright.
[1] And earlier revisions can be found here: https://eur-lex.europa.eu/procedure/EN/2016_280