My friend and I had an argument whether the usage of the phrase, "It is people like you that..." was correct. I insisted that since the subject was people, a plural, the corresponding verb could not be singular - is. His argument was that 'people like you' should treated as a group. Please advise.
It is people like you [who cause problems].
This is an it-cleft construction where the subject is not "people", but the dummy pronoun "it".
The noun phrase "people like you" functions as predicative complement of "is". Singular PCs are also possible as in It is Sue who likes you.
The bracketed element is a non-modifying relative clause, with people like you as antecedent of "who".
The comment is correct and precise.
The usage is most often to disparage "Those people" as a group. Making such generalizations of folks is a lazy means of pigeon-holing them so as to ignore their opinions or concerns. I do my best not to be one of those people.