The influence of public pressure on the investigation

I read the news about high-profile cases and noticed that scandals and public pressure are being organized around certain criminal proceedings against the prosecutor's office and the court. Please tell me, can such an information campaign or mass posts on social media really influence the course of an investigation or a court decision in our country? If so, how are the participants in the process protected from such interference, and what are the guarantees of impartiality?