Is there a single word or expression for people who share similar interests? Can the word "alike" be used in this case?
Birds of a feather
I can't really help much without more context but you're probably looking for like-minded, defined by the online Merriam-Webster as
having a like disposition or purpose : of the same mind or habit of thought
She enjoyed the club because she could meet like-minded people.
homogeneous adjective uk /ˌhɒm.əˈdʒiː.ni.əs/ /ˌhəʊ.mə-/ us /ˌhoʊ.moʊˈdʒiː-/ › consisting of parts or people that are similar to each other or are of the same type: a homogeneous group/society The population of the village has remained remarkably homogeneous. Compare (Definition of homogeneous from the Cambridge Academic Content Dictionary © Cambridge University Press)