edit: Found it: https://www.supremecourt.gov/opinions/19pdf/17-1618_hfci.pdf
Kavanaugh's dissent (p. 145ff.) appears to revolve around it being not the proper province of the Supreme Court to decide the extent of Title VII, which, IANAL but that seems like a weak dodge. The whole point of the Supreme Court is to finally decide among competing interpretations of extant legislation.
Alito's and Thomas's dissent (pp. 38-144) appears to rely on the same strict-constructionist interpretation. Its Appendix A cites a stack of dictionaries. So there's that, I guess. Appendix D is an application for employment in the US armed forces. Presumably the body of the dissent explains what this is meant to prove, although I doubt I would feel myself enlightened for the effort of going back and finding that exegesis.