by the way, in case anyone doubts the part about male versus female contacts making a difference, here's the relevant snippets:

The independent transgender identity penalty, T (1), varies little by contact person sex: among applicants who pass and disclose a male-to-female name change, discrimination estimates are nearly identical for postings listing male and female contacts. By contrast, among applicants who do not disclose a name change, the non-passing penalty is close to zero for postings listing female contacts but 8.8 pp for those listing male contacts, a statistically significant difference of 7.9 pp.

Among strongly non-passing applicants who do not disclose a name change, the penalty is 14.3 pp with a male contact and 1.8 pp with a female contact, a difference of 12.5 pp. The corresponding difference among moderately non-passing applicants is only 3.0 pp and statistically insignificant.

(emphasis mine)