I vote liberal parties in my country and that has done jack shit to prevent shitty laws to be passed because the majority seems to be electing the types of people who absolutely adore surveillance.
https://en.wikipedia.org/wiki/File:Organs_of_the_European_Un...
To the extent that conspiracies of “deep state” or “lobbyist” are involved, the only reason the EU is different to the member states themselves is that it’s a single big target instead of a lot of small ones.
Confusingly, there's also the European Council. You vote out your representative in there by voting out your your head of government (president, premier, taoiseach etc.), because again, it's literally the same person.
And if you're talking about the commission, which seems to have little to do with this, you vote them out by voting in different heads of government (again) to nominate different commissioners/a different president, and/or different members of the European parliament to not confirm them.