Quite apart from the fact that some people -- well, me certainly -- think that the statement "the bankers run the world" is factually mistaken and based on a view of how capitalism works that is -- at least to my mind -- not only naive and fundamentally flawed, but also dangerously attractive to populists of both the left and right, you do now know that a lot of people do consider the trope antisemitic -- I've already mentioned the controversy in the UK about Jeremy Corbyn's initial support for this mural:
en.wikipedia.org
Also, you may recall the response when Donald Trump suggested much the same thing in his closing campaign ad of 2016
Donald Trump has released what seems like the closing-argument ad of his campaign, and several people are pointing out that the whole thing has rather...
slate.com
(A good example, incidentally, of how it's a trope popular with antisemites on both the left and the right).
I don't presume to speak for Beebo, but I wouldn't describe it as "a dog-whistle" in the way you used it, because that suggests an element of intentionality, and I certainly wouldn't want to ascribe malign motivations to you.
However, throughout my life I've been discovering that turns of phrase and assumptions I'd grown up considering perfectly innocuous and in everyday use do not, in fact, always seem that way to other people, which is hardly surprising, when you come to think of what was considered normal and acceptable in polite society during the 1950s and 60s.
Whenever someone's pointed out to me what I'm doing, my automatic response has always been to apologise for my thoughtless and ill-chosen words, to explain I hope that my interlocutor will accept that no offence was intended, and to make a mental note not to use that particular phrase or trope in future unless I actually do want to offend people -- that's basic good manners, as far as I'm concerned.
It's not difficult to discover why many people do perceive antisemitic overtones in the "bankers rule the world" trope, combining as it does the idea of an international conspiracy to rule the world, as outlined in the Tsarist forgery, The Protocols of the Elders of Zion, with the traditional association between Jews and finance.
If you're interested, you can find very illuminating discussions of its history and how and why it's thought to lead all too easily to overt antisemitism in both Antony Julius'
Trials of the Diaspora: A History of Anti-Semitism in England and Deborah Lipstadt's
Antisemitism here and now.