Geoffrey Pullum, Professor of General Linguistics at the University of Edinburgh, wrote the following about a very similar pair of sentences (source, pages 41–43):
(1) We are talking about a man who everyone seems to think will one day be king.
(2) We are talking about a man whom everyone seems to think will one day be king.
The rule "use who for subjects and whom for nonsubjects" is insufficiently explicit. These examples involve a relative clause that begins after the word man. The next word (who or whom) introduces the relative clause (everyone seems to think __ will one day be king). There are two things that "subject" might mean here: "subject of its clause," that is, subject of the clause that it logically belongs to, or "subject of the relative clause." The word who is logically the subject in a clause that has will one day be king as its predicate; if that allows it to count as a subject, then version (1) is correct. But the subject of the whole relative clause is not who but rather everyone. The word who is not the logical subject of that, but just of a piece of it. If that's what we mean by being a subject, then we should pick sentence (2).
Where do we turn to decide this point? We look in good manuals of English usage. And we immediately find something very interesting: there are clear examples of both types in literary works by the best authors. The who group—those whose writing suggests that they would plump for (1)—includes Arnold Bennett, Charles Dickens, Henry Fielding, and William Safire (the New York Times's language pundit). Good company. But the whom group, whose usage shows they would select (2), includes early writers like William Caxton and Izaak Walton, famous novelists like Charles Kingsley and Rudyard Kipling, romantic poets like John Keats and Percy Bysshe Shelley, and at least some New York Times and Publishers Weekly writers, together with Charles Darwin and William Shakespeare. That, too, is a dream team.
What is going on? The answer is that there are two different rules involved. Some writers follow one, while others follow the other. The members of the who group tacitly assume that who has to be the subject of its clause; the members of the whom group tacitly assume that who has to be the subject of the relative clause.
Bold emphasis mine.
In short, some speakers prefer who and others prefer whom.
Following the above analysis, in the relative clause most people think __ is at the peak of her career there are two subjects. Those speakers who consider who (the lexeme) the relevant subject (the logical subject of [who] is at the peak of her career) use the nominative alternation, who, while those who consider most people the relevant subject (the subject of the entire relative clause) use the accusative alternation, whom.