UChicago students don’t need to declare a major as part of the application process and, barring one exception that I know of, are welcome to major in whatever they wish to. Many explore and change their minds or don’t make a decision till well into sophomore year. The only potential evidence I know of is from the dean of admissions who, in the context of discussing their Test Optional policy introduced a couple of admissions cycles ago with the Class of '23, mentioned that those declining to submit scores were more likely to be humanities majors while those submitting scores were more likely to be doing science. We don’t have the data to understand yet how that will play out because it appears that that over 2/3 of the class of '23 has yet to declare a major! Does that mean there are a bunch of hum kids still shopping around? Who knows? So that’s a TBD.
The common wisdom is that hum guys and stem gals will have an edge, all else equal, since it’s a holistic admissions process, but not sure that’s supported by the data. Over the past 17 years, males have made up just under 42% of Hum first majors. It’s gone up and down over the years but it hasn’t consistently been dropping, despite the large increase in enrollments by the College and the overall shift toward non-hum (as a first major) AND the introduction of and growth in CS and molecular engineering.
What IS interesting is that since the current admissions dean took over in 2008/2009, the percentage of those graduating with a hum major has stabilized from a noticeable decline earlier. In 2004, 27.2% of the College graduated with a hum (first) major. That percentage was down to 20.8% nine years later. Beginning in 2012-13, the number of applications began to skyrocket due to new admissions marketing policies and outreach under the new dean, and the College started graduating classes admitted under the new admissions department. While the percentage of the graduating class in a hum major still declined, it was far more gradual. Most recent data is the Class of 2020 and hum (first) majors were 18.6% of the total (compared to 20.8% in 2013). And this despite continued growth in the size of the College. So the data are consistent with some management going on. It’s possible, for instance, that they’ve been striving to keep a relatively diversified class across the academic divisions so choose those qualified candidates who have interests and skill sets that support that sort of diversification.
Not sure how some of those percentage are being calculated as physical sciences and Math/stats, combined are about 25%, not 18%. Perhaps there are more majors in the physical sciences at UChicago than at Stanford? The percentage breakout (recent) is bio sciences (including biology and neuro) 10%, humanities 19%, Physical sciences/Math Stats 25% and social sciences 46%. I think that this distribution is all that different from Stanford, especially if humanities for the latter suddenly jumped from 11% to 15%! 
I think the two schools are distinct from one another, but similar trends and student interests impact both schools.