Forgive my cynicism, but I don't think civil rights are the driver here, so much as that the Democrats are maybe showing slightly better forecasting skills when it comes to working with the EU.
GDPR is a harmonisation and slight update of various national laws - the UK Data Protection Act 1988, and others from France, Germany etc., with provisions added to accommodate the increased fluidity of data over the internet. As such, it's a starting point.
Currently, data cannot be exported without the subject's explicit permission. It's not that hard to see the law extended to state that, even if permission is given, it may only be exported to locations that provide equivalent data protection. Meaning that the US would not be a legal destination for data warehousing and analytics.
Outside the US, the EU is the largest consumer of US internet services. That would be a hefty blow to the bottom line. That it may help you guys a little with your privacy is a nice side effect