Normally, if you compile the same code twice on the same machine, you'll get the same result, even if it's not truly reproducible across machines or large gaps in time. And differences between machines or across time are usually small enough that they don't impact the observed behavior of the code, especially if you pin your dependencies.
However, with LaTeX, the output of the first run is often an input to the second run, so you get notably different results if you only compile it once vs. compiling twice. When I last wrote LaTeX about ten years ago, I usually encountered this with page numbers and tables of context, since the page numbers couldn't be determined until the layout was complete. So the first pass would get the bulk of the layout and content in place, and then the second pass would do it all again, but this time with real page numbers. You would never expect to see something like this in a modern compiler, at least not in a way that's visible to the user.
(That said, it's been ten years, and I never compiled anything as long or complex as a PhD thesis, so I could be wrong about why you have to compile twice.)