If culturally-discriminating WASP admissions officers were the main barrier, one would not expect non-Jewish whites to be the most underrepresented group in the Ivy League. Circa 2019, looking at non-international students only:
Ivy League US Ratio Mean SAT score [1]
Jewish 17.2% 2.4% 7.16 n/a
Asian 19.6% 5.3% 3.71 1216
White (incl. Jewish) 50.3% 61.5% 0.82 1148
Hispanic 11.4% 17.6% 0.65 1043
Black 7.8% 12.7% 0.61 966
White (non-Jewish) 33.1% 59.1% 0.56 ~1141 (lower estimate)
Percentages don't sum to 100 because multi-ethnic students, a few minor ethnicities (American-Indian, Pacific Islander..), and students categorized as "unknown"/"other" by the universities were excluded. Data on university undergraduate demographics was taken from the universities own diversity reports. Jewish representation was gathered from
http://hillel.org/college-guide/list/,
https://forward.com/jewish-college-guide/, and
https://ejewishphilanthropy.com/how-many-jewish-undergraduat..., taking the
lowest estimate when sources conflicted. ejewishphilanthropy.com (eJP) points out flaws in Hillel's data gathering (e.g. showing Harvard as 30% Jewish, when eJP found it only 16%) Hillel seems to have since fixed these flaws, as the estimates they now give are in-line with those of eJP.
[1] https://www.ednc.org/eraceing-inequities-the-influence-of-ra...