if らしく already gives the meaning of “seeming, characteristic of, ish,” etc then what is the purpose of adding 感じの？
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It emphasizes the subjective nature of the statement. If one simply said なんか男らしくない人, that would be something like "a vaguely unmasculine person," "a person somehow lacking in masculinity," etc. なんか男らしくない感じの人 is more like "a person who seems vaguely unmasculine," "a person who seems somehow lacking in masculinity."