Yes
Article 22 of the GDPR. Essentially it sates that if automated decision making occurs, you must be able to appeal to a human.
https://www.gdpr-toolkit.co.uk/individuals-rights/the-rights...
This is aside from common law, which might give some protection in that entities managing your goods (and maybe your data?), even voluntarily, have a have a duty of care to keep them safe.
All of this falls apart if the goods/service is free... And one can't really argue Google is a monopoly with regards to email services (search and ads are quite separate).
So I doubt EU could do anything about it unless one uses paid services.
Just because a service is free does not mean consumer protection and data protection laws (including GDPR) no longer apply.
Why would you think otherwise?