How "not long ago" are you thinking of? Clinton was first a major figure in the 90s (and we also had https://en.wikipedia.org/wiki/The_Fresh_Prince_of_Bel-Air ). And Clinton herself is from the baby boom generation; what male Hil(l)arys from that cohort do you have in mind?

Looks like it flipped in ~the 40s, by the ~60s had become rarer as a male name, and was pretty much a flop as a male name after the ~80s. So Clinton was born just when it started to take off for females (and in general - it was never as common as a male name) and there should have been in the same ballpark as as many male "Hilary"s of the same age.

https://namedaisy.com/us/name/Hilary

Hilary Putnam (famous male philosopher) was born in 1926. I imagine soon after this generation is flipped.