How will search results from Google/Bing etc be affected by GDPR?

GDPR needs consent in order to process personally identifiable information so lets say they scrape my personal CV site, or something else, will they actually require my consent before I'm available in the search results. This was just an example but the scrapers can hit on so much data that could be deemed personal. Is the inclusion of a robots.txt allow somehow to be taken as a form of consent here?

I saw that Googles AMP now includes a GDPR component[0] is this their way of trying to mitigate this? By having _all_ sites use AMP?

[0] https://searchengineland.com/googles-amp-project-announces-new-consent-component-ahead-of-gdpr-compliance-deadline-295633