As I understand it, Article 11 (the "link tax") is actually fairly tame. It only requires reimbursement for "use" and explicitly permits linking and citations. The term "use" is a bit ambiguous but it seems to be more directed at scraping and republishing rather than mere link aggregation. It's not a link tax.

Article 13 however still sounds worrying. It describes automated image recognition (i.e. an upload filter) as a possible mechanism for preventing the upload and publishing of illegal content. However I can't find any language that explicitly requires the filtering, non-commercial platforms like Wikipedia are explicitly exempt and it's fairly directly aimed at companies that make money from publishing content users upload to make them liable for the content they're hosting.

I'm not a lawyer, but it seems like it will mostly be trouble for companies like Facebook, Instagram, YouTube and file hosters (e.g. Mega). How dangerous it is to startups exactly depends on how "appropriate and proportionate measures leading to the non-availability on those services of works or other subject matter infringing copyright or related-rights, while non-infringing works and other subject matter shall remain available" is to be interpreted in practice.

EDIT: To clarify: I'm skeptical of this and was extremely biased against this because of what the EFF and others have said about it. But the final text seems far less terrible than the first draft that everyone got up in arms over.