Like-mindedly is a word that refers to individuals who share the same opinions or beliefs. Synonyms for this term can include harmoniously, agreeably, sympathetically, similarly, uniformly and consonantly. All these words denote an agreement in ideas, opinions, thoughts, and attitudes.
The word harmoniously suggests a musical connection between like-minded people; agreeably focuses on people's personal inclinations towards similar viewpoints, sympathetically means sharing feelings of understanding or compassion towards others' opinions, similarly shows having the same kind of opinions, uniformly speaks of people's beliefs being alike, and consonantly suggests that everyone's thoughts and beliefs are in agreement. Whatever word is used to describe a group of individuals with similar ideas, the common denominator is that they are all in accord and share a mutual mindset.