Oliver has always had an obsession with image
that(等於image) made would-be fans a little uneasy.
關係代名詞

等於
Oliver has always had an obsession with image
and image(主詞) made(動詞) would-be(形容詞) fans(名詞) a little uneasy.

Oliver一直以來對image(偶像或影像)著迷，而image讓(make/make)想(或可能)成為歌迷或影迷的人uneasy(心神不安或不自在)