I am among the "weirdos", I am an Architect! And I was the second one to join the McKinsey Madrid office, and only one after grad (the other one, and some who came after, where coming from MBAs)
As you very well say, never would I have tought when I started my 6-years studies to end up in consulting, I didn´t even know what this was!
However, it was not a 180º round done within one day, but a gradual transition: I realized that I liked project management and construction planning and optimization instead of design, I started exploring some management engenieering subjects... and ended up in the McKinsey Atrévete, a workshop for students. There was where I really learned what being a consultant was.
The journey in McKinsey and later in Amazon has been marvelous, full of insights of so many different things. This was precisely what I loved about studying Architecture, since I loved the multi-multidisciplinary approach: from Math to History, from Construction to Aesthetics. However, I realized that, when it comes to working as an architect, the scope narrows down a lot. Hence, this was the key driver why I wanted to transition to consulting is to keep the multi-discipline and multi-industry focus.
Regarding the application, people always looked at me very weridly, in all interviews and processes. However, being a non-conventional profile can be a super good asset if you know how to play it.
Hope it helps you!